| Title: | Life Insurance Premium and Reserves Valuation |
|---|---|
| Description: | Methods for valuation of life insurance premiums and reserves (including variable-benefit and fractional coverage) based on "Actuarial Mathematics" by Bowers, H.U. Gerber, J.C. Hickman, D.A. Jones and C.J. Nesbitt (1997, ISBN: 978-0938959465), "Actuarial Mathematics for Life Contingent Risks" by Dickson, David C. M., Hardy, Mary R. and Waters, Howard R (2009) <doi:10.1017/CBO9780511800146> and "Life Contingencies" by Jordan, C. W (1952) <doi:10.1017/S002026810005410X>. It also contains functions for equivalent interest and discount rate calculation, present and future values of annuities, and loan amortization schedule. |
| Authors: | Joaquin Auza [aut, cre], Maria Sol Alvarez [aut] |
| Maintainer: | Joaquin Auza <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.3 |
| Built: | 2024-11-08 03:11:21 UTC |
| Source: | https://github.com/joaquinauza/detlifeinsurance |
Calculates the present value of a life annuity.
a(x, h, n, k = 1, i = 0.04, data, prop = 1, assumption = "none", cap = 1)a(x, h, n, k = 1, i = 0.04, data, prop = 1, assumption = "none", cap = 1)
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of payments per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age, and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
cap |
A numeric type value. The annualized value of the payment. |
Returns a numeric value (actuarial present value).
Chapter 2 of Life Contingencies (1952) by Jordan, chapter 5 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
a(20,0,15,1,0.04,CSO58FALB,1,"none",1200) a(23,7,9,1,0.04,GAM71F,1,"none",5000) a(33,3,10,4,0.04,CSO80MANB,1,"constant",3000) a(20,5,10,4,0.04,CSO58MANB,1,"UDD",5000)a(20,0,15,1,0.04,CSO58FALB,1,"none",1200) a(23,7,9,1,0.04,GAM71F,1,"none",5000) a(33,3,10,4,0.04,CSO80MANB,1,"constant",3000) a(20,5,10,4,0.04,CSO58MANB,1,"UDD",5000)
Calculates the present value of the life insurance.
A.(x, h, n, k = 1, i = 0.04, data, prop = 1, assumption = "none", cap = 1)A.(x, h, n, k = 1, i = 0.04, data, prop = 1, assumption = "none", cap = 1)
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of fractions per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
cap |
A numeric type value. The value of the payment. |
Returns a numeric value (actuarial present value).
Chapter 3 of Life Contingencies (1952) by Jordan, chapter 4 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
A.(50,0,8,1,0.04,CSO80MANB,1,"none",1) A.(60,3,10,1,0.04,CSO80MANB,1,"none",1) A.(21,4,7,3,0.04,CSO80MANB,1,"constant",1) A.(23,4,6,12,0.04,CSO80MANB,1,"UDD",1)A.(50,0,8,1,0.04,CSO80MANB,1,"none",1) A.(60,3,10,1,0.04,CSO80MANB,1,"none",1) A.(21,4,7,3,0.04,CSO80MANB,1,"constant",1) A.(23,4,6,12,0.04,CSO80MANB,1,"UDD",1)
Calculates the present value of a continuous life annuity.
aCont(x, h, n, i = 0.04, data, prop = 1, assumption = "constant", cap = 1)aCont(x, h, n, i = 0.04, data, prop = 1, assumption = "constant", cap = 1)
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
i |
The interest rate. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths and "constant" for constant force of mortality). |
cap |
A numeric type value. The value of the payment. |
Returns a numeric value (the actuarial present value).
Chapter 2 of Life Contingencies (1952) by Jordan, chapter 5 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
aCont(35,7,10,0.04,CSO80MANB,1,"constant",1) aCont(23,5,12,0.04,CSO80MANB,1,"UDD",1)aCont(35,7,10,0.04,CSO80MANB,1,"constant",1) aCont(23,5,12,0.04,CSO80MANB,1,"UDD",1)
Calculates the present value of a continuous life insurance.
ACont.(x, h, n, i = 0.04, data, prop = 1, assumption = "UDD", cap = 1)ACont.(x, h, n, i = 0.04, data, prop = 1, assumption = "UDD", cap = 1)
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
i |
The interest rate. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths and "constant" for constant force of mortality). |
cap |
A numeric type value. The value of the payment. |
Returns a numeric (actuarial present value).
Chapter 3 of Life Contingencies (1952) by Jordan, chapter 4 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
ACont.(24,2,10,0.04,CSO80MANB,1,"UDD",1) ACont.(24,2,10,0.04,CSO80MANB,1,"constant",1)ACont.(24,2,10,0.04,CSO80MANB,1,"UDD",1) ACont.(24,2,10,0.04,CSO80MANB,1,"constant",1)
Calculates the present value of a decreasing life annuity.
aD( x, h, n, k = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap = 1 )aD( x, h, n, k = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap = 1 )
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of payments per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
variation |
A character string. "inter" if the variation it's interannual or "intra" if it's intra-annual. |
cap |
A numeric type value. The annualized value of the first payment. |
Returns a numeric value (actuarial present value).
Chapter 2 of Life Contingencies (1952) by Jordan, chapter 5 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
aD(27,0,3,1,0.04,CSO80MANB,1,"none","none",1) aD(32,2,8,1,0.04,CSO80MANB,1,"none","none",1) aD(35,8,15,4,0.04,CSO80MANB,1,"constant","inter",1) aD(21,2,5,4,0.04,CSO80MANB,1,"UDD","inter",1) aD(54,4,16,2,0.04,CSO80MANB,1,"constant","intra",1) aD(20,10,15,3,0.04,CSO80MANB,1,"UDD","intra",1)aD(27,0,3,1,0.04,CSO80MANB,1,"none","none",1) aD(32,2,8,1,0.04,CSO80MANB,1,"none","none",1) aD(35,8,15,4,0.04,CSO80MANB,1,"constant","inter",1) aD(21,2,5,4,0.04,CSO80MANB,1,"UDD","inter",1) aD(54,4,16,2,0.04,CSO80MANB,1,"constant","intra",1) aD(20,10,15,3,0.04,CSO80MANB,1,"UDD","intra",1)
Calculates the present value of a decreasing life insurance.
AD.( x, h, n, k = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap = 1 )AD.( x, h, n, k = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap = 1 )
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Fractions per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
variation |
A character string. "inter" if the variation it's interannual or "intra" if it's intra-annual. |
cap |
A numeric type value. Amount insured for the first year/period. |
Returns a numeric value (actuarial present value).
Chapter 3 of Life Contingencies (1952) by Jordan, chapter 4 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
AD.(56,0,8,1,0.04,CSO80MANB,1,"none","none",1) AD.(39,1,10,1,0.04,CSO80MANB,1,"none","none",1) AD.(37,6,11,4,0.04,CSO80MANB,1,"constant","inter",1) AD.(21,2,5,4,0.04,CSO80MANB,1,"UDD","inter",1) AD.(54,4,16,2,0.04,CSO80MANB,1,"constant","intra",1) AD.(20,10,15,3,0.04,CSO80MANB,1,"UDD","intra",1)AD.(56,0,8,1,0.04,CSO80MANB,1,"none","none",1) AD.(39,1,10,1,0.04,CSO80MANB,1,"none","none",1) AD.(37,6,11,4,0.04,CSO80MANB,1,"constant","inter",1) AD.(21,2,5,4,0.04,CSO80MANB,1,"UDD","inter",1) AD.(54,4,16,2,0.04,CSO80MANB,1,"constant","intra",1) AD.(20,10,15,3,0.04,CSO80MANB,1,"UDD","intra",1)
Calculates the present value of an annuity.
af(l = 0, n, i)af(l = 0, n, i)
l |
0 for annuity due or 1 for annuity immediate. |
n |
A numeric value. The number of payments. |
i |
A numeric value. The interest rate. |
af(0,10,0.03) af(1,15,0.05)af(0,10,0.03) af(1,15,0.05)
Calculates the present value of a life annuity for a group.
am( x, h, n, k = 1, i = 0.04, data, prop = 1, type = "joint", quant = 1, assumption = "none", cap = 1 )am( x, h, n, k = 1, i = 0.04, data, prop = 1, type = "joint", quant = 1, assumption = "none", cap = 1 )
x |
A vector of intergers representing the age of each individual of the group. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of payments per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age, and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
type |
A character string. Conditions to be met in order to access the benefit of the annuity ("joint", "exactly" or "atleast"). |
quant |
An integer. Required only if type is not "joint". If type is "exactly" it represents the exact amount of survivors required for the endowment to be payed. If type is "atleast", it represents the minimum number of survivors required. |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
cap |
A numeric type value. The annualized value of the payment. |
Returns a numeric value (actuarial present value).
ages<-c(23,34,21) ages<-c(23,34,21) am(ages,5,10,2,0.05,CSO80MALB,1,"joint",assumption="UDD") am(ages,0,20,1,0.06,CSO80FALBsmoker,1,"atleast",1) am(ages,2,15,2,0.07,CSO80FANBsmoker,0.8,"exactly",2,"constant")ages<-c(23,34,21) ages<-c(23,34,21) am(ages,5,10,2,0.05,CSO80MALB,1,"joint",assumption="UDD") am(ages,0,20,1,0.06,CSO80FALBsmoker,1,"atleast",1) am(ages,2,15,2,0.07,CSO80FANBsmoker,0.8,"exactly",2,"constant")
Calculates the present value of a life insurance coverage for a group.
Am.( x, h, n, k = 1, i = 0.04, data, prop = 1, ndeath = 1, assumption = "none", cap = 1 )Am.( x, h, n, k = 1, i = 0.04, data, prop = 1, ndeath = 1, assumption = "none", cap = 1 )
x |
A vector of intergers representing the age of each individual of the group. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of fractions per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
ndeath |
An integer. Number of deaths necessary for payment to occur. |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
cap |
A numeric type value. The value of the payment. |
Returns a numeric value (actuarial present value).
ages<-c(22,33,44,55,66) Am.(ages,5,15,1,0.04,CSO80MANB,1,2,"none",1) Am.(ages,0,20,4,0.04,CSO80MANB,1,2,"UDD",1) Am.(ages,10,25,2,0.04,CSO80MANB,1,2,"constant",1)ages<-c(22,33,44,55,66) Am.(ages,5,15,1,0.04,CSO80MANB,1,2,"none",1) Am.(ages,0,20,4,0.04,CSO80MANB,1,2,"UDD",1) Am.(ages,10,25,2,0.04,CSO80MANB,1,2,"constant",1)
Mortality table (ultimate): Argentina Instituto Nacional de Estadistica y Censos (INDEC). Nation: Argentina. Year: 1990-1992. Sex: Males and Females Combined.
data(ArgentinaINDEC9092comb)data(ArgentinaINDEC9092comb)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20003
Mortality table (ultimate): Argentina Instituto Nacional de Estadistica y Censos (INDEC). Nation: Argentina. Year: 1990-1992. Sex: Female.
data(ArgentinaINDEC9092F)data(ArgentinaINDEC9092F)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20002
Mortality table (ultimate): Argentina Instituto Nacional de Estadistica y Censos (INDEC). Nation: Argentina. Year: 1990-1992. Sex: Male.
data(ArgentinaINDEC9092M)data(ArgentinaINDEC9092M)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20001
Calculates the present value of a varying life annuity according to a arithmetic progression.
av( x, h, n, k = 1, r = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap = 1 )av( x, h, n, k = 1, r = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap = 1 )
x |
An integer. The age on the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of payments per year. |
r |
The variation rate. A numeric type value. |
i |
The interest rate. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
variation |
A character string. "inter" if the variation it's interannual or "intra" if it's intra-annual. |
cap |
A numeric type value. The annualized value of the first payment. |
Returns a numeric value (actuarial present value).
For an increasing life annuity coverage, 'r' must be 1.
Chapter 5 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
av(33,0,5,1,0.8,0.04,CSO80MANB,1,"none","none",1) av(26,2,4,1,0.4,0.04,CSO80MANB,1,"none","none",1) av(26,1,5,4,0.5,0.04,CSO80MANB,1,"constant","inter",1) av(24,1,3,3,0.7,0.04,CSO80MANB,1,"constant","intra",1) av(35,4,6,6,0.4,0.04,CSO80MANB,1,"UDD","inter",1) av(40,3,7,2,0.7,0.04,CSO80MANB,1,"UDD","intra",1)av(33,0,5,1,0.8,0.04,CSO80MANB,1,"none","none",1) av(26,2,4,1,0.4,0.04,CSO80MANB,1,"none","none",1) av(26,1,5,4,0.5,0.04,CSO80MANB,1,"constant","inter",1) av(24,1,3,3,0.7,0.04,CSO80MANB,1,"constant","intra",1) av(35,4,6,6,0.4,0.04,CSO80MANB,1,"UDD","inter",1) av(40,3,7,2,0.7,0.04,CSO80MANB,1,"UDD","intra",1)
Calculates the present value of a varying life insurance according to a arithmetic progression.
Av.( x, h, n, k = 1, r = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap = 1 )Av.( x, h, n, k = 1, r = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap = 1 )
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Fractions per year. |
r |
The variation rate. A numeric type value. |
i |
The interest rate. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
variation |
A character string. "inter" if the variation it's interannual or "intra" if it's intra-annual. |
cap |
A numeric type value. Amount insured for the first year/period. |
Returns a numeric value (actuarial present value).
For an increasing life insurance coverage, 'r' must be 1.
Chapter 4 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Av.(43,0,4,1,0.7,0.04,CSO80MANB,1,"none","none",1) Av.(37,1,6,1,0.3,0.04,CSO80MANB,1,"none","none",1) Av.(25,2,3,2,0.6,0.04,CSO80MANB,1,"constant","inter",1) Av.(37,3,6,4,0.5,0.04,CSO80MANB,1,"constant","intra",1) Av.(40,3,5,2,0.4,0.04,CSO80MANB,1,"UDD","inter",1) Av.(50,2,4,4,0.6,0.04,CSO80MANB,1,"UDD","intra",1)Av.(43,0,4,1,0.7,0.04,CSO80MANB,1,"none","none",1) Av.(37,1,6,1,0.3,0.04,CSO80MANB,1,"none","none",1) Av.(25,2,3,2,0.6,0.04,CSO80MANB,1,"constant","inter",1) Av.(37,3,6,4,0.5,0.04,CSO80MANB,1,"constant","intra",1) Av.(40,3,5,2,0.4,0.04,CSO80MANB,1,"UDD","inter",1) Av.(50,2,4,4,0.6,0.04,CSO80MANB,1,"UDD","intra",1)
Calculates the present value of a varying life annuity according to a geometric progression.
avg( x, h, n, k = 1, r, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap = 1 )avg( x, h, n, k = 1, r, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap = 1 )
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of payments per year. |
r |
The variation rate. A numeric type value. |
i |
The interest rate. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
variation |
A character string. "inter" if the variation it's interannual or "intra" if it's intra-annual. |
cap |
A numeric type value. The annualized value of the first payment. |
Returns a numeric value (actuarial present value).
Chapter 5 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
avg(33,0,5,1,0.8,0.04,CSO80MANB,1,"none","none",1) avg(26,2,4,1,0.4,0.04,CSO80MANB,1,"none","none",1) avg(20,2,2,2,0.15,0.04,CSO80MANB,1,"constant","inter",1) avg(40,5,5,3,0.07,0.04,CSO80MANB,1,"constant","intra",1) avg(27,0,15,4,0.06,0.04,CSO80MANB,1,"UDD","inter",1) avg(34,7,12,6,0.03,0.04,CSO80MANB,1,"UDD","intra",1)avg(33,0,5,1,0.8,0.04,CSO80MANB,1,"none","none",1) avg(26,2,4,1,0.4,0.04,CSO80MANB,1,"none","none",1) avg(20,2,2,2,0.15,0.04,CSO80MANB,1,"constant","inter",1) avg(40,5,5,3,0.07,0.04,CSO80MANB,1,"constant","intra",1) avg(27,0,15,4,0.06,0.04,CSO80MANB,1,"UDD","inter",1) avg(34,7,12,6,0.03,0.04,CSO80MANB,1,"UDD","intra",1)
Calculates the present value of a varying life insurance according to a geometric progression.
Avg.( x, h, n, k = 1, r, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap = 1 )Avg.( x, h, n, k = 1, r, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap = 1 )
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Fractions per year. |
r |
The variation rate. A numeric type value. |
i |
The interest rate. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
variation |
A character string. "inter" if the variation it's interannual or "intra" if it's intra-annual. |
cap |
A numeric type value. Amount insured for the first year/period. |
Returns a numeric value (actuarial present value).
Chapter 4 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Avg.(33,0,5,1,0.8,0.04,CSO80MANB,1,"none","none",1) Avg.(26,2,4,1,0.4,0.04,CSO80MANB,1,"none","none",1) Avg.(25,0,15,2,0.25,0.04,CSO80MANB,1,"constant","inter",1) Avg.(37,10,10,4,0.05,0.04,CSO80MANB,1,"constant","intra",1) Avg.(40,5,20,6,0.04,0.04,CSO80MANB,1,"UDD","inter",1) Avg.(20,0,80,12,0.01,0.04,CSO80MANB,1,"UDD","intra",1)Avg.(33,0,5,1,0.8,0.04,CSO80MANB,1,"none","none",1) Avg.(26,2,4,1,0.4,0.04,CSO80MANB,1,"none","none",1) Avg.(25,0,15,2,0.25,0.04,CSO80MANB,1,"constant","inter",1) Avg.(37,10,10,4,0.05,0.04,CSO80MANB,1,"constant","intra",1) Avg.(40,5,20,6,0.04,0.04,CSO80MANB,1,"UDD","inter",1) Avg.(20,0,80,12,0.01,0.04,CSO80MANB,1,"UDD","intra",1)
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Female. Basis: Age Last Birthday. Smoker: No.
data(CSO2001FALBnonsmoker)data(CSO2001FALBnonsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1517
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Female. Basis: Age Last Birthday. Smoker: yes.
data(CSO2001FALBsmoker)data(CSO2001FALBsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1519
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Female. Basis: Age Nearest Birthday. Smoker: No.
data(CSO2001FANBnonsmoker)data(CSO2001FANBnonsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1140
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Female. Basis: Age Nearest Birthday. Smoker: Yes.
data(CSO2001FANBsmoker)data(CSO2001FANBsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1141
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Male. Basis: Age Last Birthday. Smoker: No.
data(CSO2001MALBnonsmoker)data(CSO2001MALBnonsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1516
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Male. Basis: Age Last Birthday. Smoker: yes.
data(CSO2001MALBsmoker)data(CSO2001MALBsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1518
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Male. Basis: Age Nearest Birthday. Smoker: No.
data(CSO2001MANBnonsmoker)data(CSO2001MANBnonsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1137
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Male. Basis: Age Nearest Birthday. Smoker: Yes.
data(CSO2001MANBsmoker)data(CSO2001MANBsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1138
Mortality table (ultimate): Commissioner's Standard Ordinary. Year: 1958. Nation: United States of America. Sex: Female. Basis: Age Last Birthday.
data(CSO58FALB)data(CSO58FALB)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=8
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1958. Sex: Female. Basis: Age Nearest Birthday.
data(CSO58FANB)data(CSO58FANB)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=6
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1958. Sex: Male. Basis: Age Last Birthday.
data(CSO58MALB)data(CSO58MALB)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=7
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1958. Sex: Male. Basis: Age Nearest Birthday.
data(CSO58MANB)data(CSO58MANB)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=5
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Female Age method: Age Last Birthday.
data(CSO80FALB)data(CSO80FALB)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=35
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Female. Basis: Age Last Birthday. Smoker: No.
data(CSO80FALBnonsmoker)data(CSO80FALBnonsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=37
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Female. Basis: Age Last Birthday. Smoker: Yes.
data(CSO80FALBsmoker)data(CSO80FALBsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=39
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Female. Basis: Age Nearest Birthday.
data(CSO80FANB)data(CSO80FANB)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=36
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Female. Basis: Age Nearest Birthday. Smoker: No.
data(CSO80FANBnonsmoker)data(CSO80FANBnonsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=38
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Female. Basis: Age Nearest Birthday. Smoker: Yes.
data(CSO80FANBsmoker)data(CSO80FANBsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=40
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Male. Basis: Age Last Birthday.
data(CSO80MALB)data(CSO80MALB)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=41
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Male. Basis: Age Last Birthday. Smoker: No.
data(CSO80MALBnonsmoker)data(CSO80MALBnonsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=43
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Male. Basis: Age Last Birthday. Smoker: Yes.
data(CSO80MALBsmoker)data(CSO80MALBsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=45
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Male. Age method: Age Nearest Birthday.
data(CSO80MANB)data(CSO80MANB)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=42
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Male. Basis: Age Nearest Birthday. Smoker: No.
data(CSO80MANBnonsmoker)data(CSO80MANBnonsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=44
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Male. Basis: Age Nearest Birthday. Smoker: Yes.
data(CSO80MANBsmoker)data(CSO80MANBsmoker)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=46
Calculates the Pure endowments.
E(x, n, i = 0.04, data, prop = 1, assumption = "none", cap = 1)E(x, n, i = 0.04, data, prop = 1, assumption = "none", cap = 1)
x |
An integer. The age of the insuree. |
n |
The term of the endowment. An integer, for annual coverage, or a numeric for fractional coverage. |
i |
The interest rate. A numeric type value. |
data |
A data.frame containing the mortality table, with the first column being the age and the second one, the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
cap |
A numeric type value. The payment. |
Chapter 2 of Life Contingencies (1952) by Jordan.
E(45,10,0.04,CSO80MANB,1,"none",1000) E(24,1.6,0.04,CSO80MANB,1,"constant",17000) E(26,2.4,0.04,CSO58FALB,1,"UDD",3500)E(45,10,0.04,CSO80MANB,1,"none",1000) E(24,1.6,0.04,CSO80MANB,1,"constant",17000) E(26,2.4,0.04,CSO58FALB,1,"UDD",3500)
Calculates the Pure endowments for a group of insurees.
Em( x, n, i = 0.04, data, prop = 1, type = "joint", quant = 1, assumption = "none", cap = 1 )Em( x, n, i = 0.04, data, prop = 1, type = "joint", quant = 1, assumption = "none", cap = 1 )
x |
A vector of integers. The age of the insurees. |
n |
The term of the endowment. An integer, for annual coverage, or a numeric for fractional coverage. |
i |
The interest rate. A numeric type value. |
data |
A data.frame containing the mortality table, with the first column being the age and the second one, the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
type |
A character string. Conditions to be met in order to access the benefit of the endowment ("joint", "exactly" or "atleast"). |
quant |
An integer. Required only if type is not "joint". If type is "exactly" it represents the exact amount of survivors required for the endowment to be payed. If type is "atleast", it represents the minimum number of survivors required. |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
cap |
A numeric type value. The payment. |
ages<-c(23,33,33) Em(ages,15,0.04,CSO80MANB,1,"joint") Em(ages,20.5,0.04,CSO80MANB,1,"joint",assumption = "constant",cap= 1) Em(ages,10.5,0.04,CSO80MANB,1,"joint",assumption = "UDD", cap=1) ages<-c(20,23,24,25) Em(ages,15,0.04,CSO80MANB,1,"exactly",1,"none",1) Em(ages,24.2,0.04,CSO80MANB,1,"exactly",2,"constant",1) Em(ages,8.2,0.04,CSO80MANB,1,"exactly",3,"UDD",1) ages<-c(40,42,56,57,58,59) Em(ages,15,0.04,CSO80MANB,1,"atleast",1,"none",1) Em(ages,25.5,0.04,CSO80MANB,1,"atleast",4,"constant",1) Em(ages,15.3,0.04,CSO80MANB,1,"atleast",3,"UDD",1)ages<-c(23,33,33) Em(ages,15,0.04,CSO80MANB,1,"joint") Em(ages,20.5,0.04,CSO80MANB,1,"joint",assumption = "constant",cap= 1) Em(ages,10.5,0.04,CSO80MANB,1,"joint",assumption = "UDD", cap=1) ages<-c(20,23,24,25) Em(ages,15,0.04,CSO80MANB,1,"exactly",1,"none",1) Em(ages,24.2,0.04,CSO80MANB,1,"exactly",2,"constant",1) Em(ages,8.2,0.04,CSO80MANB,1,"exactly",3,"UDD",1) ages<-c(40,42,56,57,58,59) Em(ages,15,0.04,CSO80MANB,1,"atleast",1,"none",1) Em(ages,25.5,0.04,CSO80MANB,1,"atleast",4,"constant",1) Em(ages,15.3,0.04,CSO80MANB,1,"atleast",3,"UDD",1)
Creates a fractional mortality table for a given mortality table.
Fractional_table(data, frac, i = 0.04, assumption = "UDD")Fractional_table(data, frac, i = 0.04, assumption = "UDD")
data |
A data.frame of the annual mortality table, with the first column being the age and the second one the probability of death. |
frac |
An integer. The number of fractions per year. |
i |
A numeric type value. The interest rate. |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths and "constant" for constant force of mortality). |
Returns a data.frame object containing fractional age and death probability vectors.
Chapter 3 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt
Fractional_table(CSO80MANB,2,0.04,"constant") Fractional_table(CSO80MANB,2,0.04,"UDD")Fractional_table(CSO80MANB,2,0.04,"constant") Fractional_table(CSO80MANB,2,0.04,"UDD")
Mortality table (ultimate): Group Annuity Mortality. Nation: United States of America. Year: 1971. Sex: Female.
data(GAM71F)data(GAM71F)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=817, http://servicios.infoleg.gob.ar/infolegInternet/anexos/80000-84999/81029/norma.htm
Mortality table (ultimate): Group Annuity Mortality. Nation: United States of America. Year: 1971. Sex: Male.
data(GAM71M)data(GAM71M)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=818, http://servicios.infoleg.gob.ar/infolegInternet/anexos/80000-84999/81029/norma.htm
Mortality table (ultimate): Group Annuity Mortality. Nation: United States of America. Year: 1983. Sex: Female.
data(GAM83F)data(GAM83F)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=825
Mortality table (ultimate): Group Annuity Mortality. Nation: United States of America. Year: 1983. Sex: Male.
data(GAM83M)data(GAM83M)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=826
Mortality table (ultimate): Group Annuity Mortality. Year: 1994. Sex: Female.
data(GAM94F)data(GAM94F)
a dataframe containing a column for age (x) and a column for death probability (q)
Mortality table (ultimate): Group Annuity Mortality. Nation: United States of America. Year: 1994. Sex: Female. Basis: Age Nearest Birthday.
data(GAM94FANB)data(GAM94FANB)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=834
Mortality table (ultimate): Group Annuity Mortality. Year: 1994. Sex: Male.
data(GAM94M)data(GAM94M)
a dataframe containing a column for age (x) and a column for death probability (q)
Mortality table (ultimate): Group Annuity Mortality. Nation: United States of America. Year: 1994. Sex: Male. Basis: Age Nearest Birthday.
data(GAM94MANB)data(GAM94MANB)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=835
Calculates the probability of survival given a mortality table for a group.
JointSurvival(x, n, data, prop = 1)JointSurvival(x, n, data, prop = 1)
x |
A vector representing the age of each individual. |
n |
An integer. The term. |
data |
A data.frame of the mortality table, with the first column being the age and the second one, the probability of death. |
prop |
A numeric value. The proportion of the mortality table used, between 0 and 1. |
ages<-c(34,45,52,65) JointSurvival(ages,10,CSO80FALB)ages<-c(34,45,52,65) JointSurvival(ages,10,CSO80FALB)
Calculates the amortization schedule.
Loan_amortization(V0, n, i, i2 = 0, alic = 0, ins = 0, method)Loan_amortization(V0, n, i, i2 = 0, alic = 0, ins = 0, method)
V0 |
A numeric type value. Loan value. |
n |
A numeric type value. The number of payments. |
i |
A numeric type value or a vector of them. The interest rate of the loan. |
i2 |
A numeric type value. The interest rate of the saving account. |
alic |
A numeric type value. Interest tax rate. |
ins |
A numeric type value. The rate of V0 to be paid in each period. |
method |
A string. Amortization method used ("constant_installment","interest_only", "constant_principal", "interest_only_wsavings_account" or "constant_installment_varintrate" ). |
Returns a data.frame object containing Period, Payment, Pure Payment, Intrest, Amortization, Insurance, TAX and Outstanding debt.
Loan_amortization(1000,12,0.04,0,0.21,0.01,"constant_installment") Loan_amortization(12000,15,0.04,0,0.21,0.01,"interest_only") Loan_amortization(13000,10,0.04,0,0.21,0.01,"constant_principal") Loan_amortization(15000,20,0.04,0.05,0.21,0.01,"interest_only_wsavings_account") Loan_amortization(5000,5,0.04,0,0.21,0.01,"constant_installment_varintrate")Loan_amortization(1000,12,0.04,0,0.21,0.01,"constant_installment") Loan_amortization(12000,15,0.04,0,0.21,0.01,"interest_only") Loan_amortization(13000,10,0.04,0,0.21,0.01,"constant_principal") Loan_amortization(15000,20,0.04,0.05,0.21,0.01,"interest_only_wsavings_account") Loan_amortization(5000,5,0.04,0,0.21,0.01,"constant_installment_varintrate")
Mortality table (ultimate): Mortalidad Activos y Pasivos. Nation: Argentina. Year: 2002-2006. Sex: Female. Status: Active.
data(MAyP0206activeF)data(MAyP0206activeF)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20005
Mortality table (ultimate): Mortalidad Activos y Pasivos. Nation: Argentina. Year: 2002-2006. Sex: Male. Status: Active.
data(MAyP0206activeM)data(MAyP0206activeM)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20004
Mortality table (ultimate): Mortalidad Activos y Pasivos. Nation: Argentina. Year: 2002-2006. Sex: Female. Status: Combined Active and Retired.
data(MAyP0206CAF)data(MAyP0206CAF)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20009
Mortality table (ultimate): Mortalidad Activos y Pasivos. Nation: Argentina. Year: 2002-2006. Sex: Male. Status: Combined Active and Retired.
data(MAyP0206CAM)data(MAyP0206CAM)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20008
Mortality table (ultimate): Mortalidad Activos y Pasivos. Nation: Argentina. Year: 2002-2006. Sex: Female. Status: Retired.
data(MAyP0206retiredF)data(MAyP0206retiredF)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20007
Mortality table (ultimate): Mortalidad Activos y Pasivos. Nation: Argentina. Year: 2002-2006. Sex: Male. Status: Retired.
data(MAyP0206retiredM)data(MAyP0206retiredM)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20006
Mortality table (ultimate): Mortalidad Invalidez. Nation: Chile. Year: 2006. Sex: Female.
data(Mi06F)data(Mi06F)
A data frame containing a column for age (x) and a column for death probability (q).
for more information on how to adjust the values of the table using an 'improvement rate' visit: https://www.spensiones.cl/portal/compendio/596/w3-propertyvalue-3537.html
https://mort.soa.org/ViewTable.aspx?&TableIdentity=2713,https://www.spensiones.cl/portal/compendio/596/w3-propertyvalue-3542.html
Mortality table (ultimate): Mortalidad Invalidez. Nation: Chile. Year: 2006. Sex: Male.
data(Mi06M)data(Mi06M)
A data frame containing a column for age (x) and a column for death probability (q).
For more information on how to adjust the values of the table using an 'improvement rate' visit: https://www.spensiones.cl/portal/compendio/596/w3-propertyvalue-3537.html
https://mort.soa.org/ViewTable.aspx?&TableIdentity=2712,https://www.spensiones.cl/portal/compendio/596/w3-propertyvalue-3542.html
Mortality table (ultimate): Mortalidad Invalidez. Nation: Chile. Year: 1985. Sex: Female.
data(Mi85F)data(Mi85F)
A data frame containing a column for age (x) and a column for death probability (q).
http://servicios.infoleg.gob.ar/infolegInternet/anexos/80000-84999/81029/norma.htm
Mortality table (ultimate): Mortalidad Invalidez. Nation: Chile. Year: 1985. Sex: Male.
data(Mi85M)data(Mi85M)
A data frame containing a column for age (x) and a column for death probability (q).
http://servicios.infoleg.gob.ar/infolegInternet/anexos/80000-84999/81029/norma.htm
Calculates the present value of the loan insurance.
Payment_Protection( x, n, k = 1, V0, i = 0.04, ip = 0.04, data, prop = 1, type = "outstanding_debt", method = "interest_only" )Payment_Protection( x, n, k = 1, V0, i = 0.04, ip = 0.04, data, prop = 1, type = "outstanding_debt", method = "interest_only" )
x |
An integer. The age of the insuree. |
n |
An integer. Loan term (in years). |
k |
An integer. Number of payments per year. |
V0 |
A numeric type value. Loan value. |
i |
The interest rate. A numeric type value. |
ip |
The interest rate of the loan. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
type |
A character string. The type of loan protection/reimburstment ("outstanding_debt" or "payments"). |
method |
A character string. Amortization scheme ("constant_instalment", "interest_only" or "constant_principal"). |
Returns a numeric value (actuarial present value).
Payment_Protection(35,2,1,1000000,0.04,0.06,CSO80MANB,1,"payments","constant_instalment") Payment_Protection(43,2,1,1000000,0.04,0.07,CSO80MANB,1,"outstanding_debt","constant_instalment") Payment_Protection(30,2,2,1000000,0.04,0.06,CSO80MANB,1,"payments","constant_instalment") Payment_Protection(20,2,2,1000000,0.04,0.07,CSO80MANB,1,"outstanding_debt","constant_instalment") Payment_Protection(33,2,1,1000000,0.04,0.05,CSO80MANB,1,"payments","interest_only") Payment_Protection(56,2,1,1000000,0.04,0.06,CSO80MANB,1,"outstanding_debt","interest_only") Payment_Protection(40,2,2,1000000,0.04,0.06,CSO80MANB,1,"payments","interest_only") Payment_Protection(25,2,2,1000000,0.04,0.05,CSO80MANB,1,"outstanding_debt","interest_only") Payment_Protection(23,2,1,1000000,0.04,0.07,CSO80MANB,1,"payments","constant_principal") Payment_Protection(35,2,1,1000000,0.04,0.06,CSO80MANB,1,"outstanding_debt","constant_principal") Payment_Protection(45,2,2,1000000,0.04,0.05,CSO80MANB,1,"payments","constant_principal") Payment_Protection(35,2,2,1000000,0.04,0.07,CSO80MANB,1,"outstanding_debt","constant_principal")Payment_Protection(35,2,1,1000000,0.04,0.06,CSO80MANB,1,"payments","constant_instalment") Payment_Protection(43,2,1,1000000,0.04,0.07,CSO80MANB,1,"outstanding_debt","constant_instalment") Payment_Protection(30,2,2,1000000,0.04,0.06,CSO80MANB,1,"payments","constant_instalment") Payment_Protection(20,2,2,1000000,0.04,0.07,CSO80MANB,1,"outstanding_debt","constant_instalment") Payment_Protection(33,2,1,1000000,0.04,0.05,CSO80MANB,1,"payments","interest_only") Payment_Protection(56,2,1,1000000,0.04,0.06,CSO80MANB,1,"outstanding_debt","interest_only") Payment_Protection(40,2,2,1000000,0.04,0.06,CSO80MANB,1,"payments","interest_only") Payment_Protection(25,2,2,1000000,0.04,0.05,CSO80MANB,1,"outstanding_debt","interest_only") Payment_Protection(23,2,1,1000000,0.04,0.07,CSO80MANB,1,"payments","constant_principal") Payment_Protection(35,2,1,1000000,0.04,0.06,CSO80MANB,1,"outstanding_debt","constant_principal") Payment_Protection(45,2,2,1000000,0.04,0.05,CSO80MANB,1,"payments","constant_principal") Payment_Protection(35,2,2,1000000,0.04,0.07,CSO80MANB,1,"outstanding_debt","constant_principal")
Calculates the annualized value of the fractional premiums.
PremiumFrac(px1, x, m, k, i = 0.04, data, prop = 1, effect = "yes", assumption)PremiumFrac(px1, x, m, k, i = 0.04, data, prop = 1, effect = "yes", assumption)
px1 |
A numeric type value. The value of the single net premium. |
x |
An integer. The age of the insuree. |
m |
An integer. Years of premium payment. |
k |
An integer. Number of premiums per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table used (between 0 and 1). |
effect |
A character string. This parameter indicates if, in the event of death, the insuree is released from paying the remaining fractional premiums of that year ("yes" or "no") |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths and "constant" for constant force of mortality). |
Returns the annualized value of the fractional premium.
If k=1, regardless of the "effect", the returned value is the annual premium.
Chapter 4 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters
PremiumFrac(1000,20,10,2,0.04,CSO80MANB,1,"yes","constant") PremiumFrac(1000,20,10,2,0.04,CSO80MANB,1,"no","UDD")PremiumFrac(1000,20,10,2,0.04,CSO80MANB,1,"yes","constant") PremiumFrac(1000,20,10,2,0.04,CSO80MANB,1,"no","UDD")
Calculates the fractional probability for a person of x+s/k dies before age x+(s+1)/k.
qfrac(x, s, k, i, data, assumption, prop)qfrac(x, s, k, i, data, assumption, prop)
x |
An integer. The age of the insuree. |
s |
An integer. Fraction of the year. |
k |
An integer. Number of fractions per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame containing the mortality table, with the first column being the age and the second one, the probability of death. |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths and "constant" for constant force of mortality). |
prop |
A numeric value. It represents the proportion of the mortality table being used (between 0 and 1). |
The fractional probability of death.
qfrac(27,1,4,0.04,CSO80MANB,"constant",1) qfrac(20,0,12,0.04,CSO80MANB,"UDD",0.8)qfrac(27,1,4,0.04,CSO80MANB,"constant",1) qfrac(20,0,12,0.04,CSO80MANB,"UDD",0.8)
Converts nominal and effective interest and discount rates.
Rate_converter(num, rate1, m, rate2, k, type = "days")Rate_converter(num, rate1, m, rate2, k, type = "days")
num |
A numeric type value. It is the interest/discount rate to be converted. |
rate1 |
A string ("i", "d","f" or "j"). Type of interest/discount rate to be converted. |
m |
number of capitalizations. |
rate2 |
A string ("i" for effective interest rate, "d" for effective discount rate,"f" for nominal discount rate, "j" for nominal interest rate).Type of interest/discount rate to obtain. |
k |
An integer. Number of capitalizations per year. |
type |
A string. Reference for "k", indicating whether it is expressed as a fraction or as days ("frac" or "days"). |
Rate_converter(0.04,"i",1,"i",6,"frac") Rate_converter(0.04,"f",1,"j",6,"frac") Rate_converter(0.04,"f",365,"d",60,"days") Rate_converter(0.04,"f",365,"f",60,"days")Rate_converter(0.04,"i",1,"i",6,"frac") Rate_converter(0.04,"f",1,"j",6,"frac") Rate_converter(0.04,"f",365,"d",60,"days") Rate_converter(0.04,"f",365,"f",60,"days")
Mortality table (ultimate): Renta Vitalicia. Nation: Chile. Year: 2004. Sex: Female.
data(RV04F)data(RV04F)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1500
Mortality table (ultimate): Renta Vitalicia. Nation: Chile. Year: 2004. Sex: Male.
data(RV04M)data(RV04M)
A data frame containing a column for age (x) and a column for death probability (q).
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1499
Calculates the future value of an annuity.
sf(l = 0, n, i)sf(l = 0, n, i)
l |
0 for annuity due or 1 for annuity immediate. |
n |
A numeric value. The number of payments. |
i |
A numeric value. The interest rate. |
sf(0,12,0.05) sf(1,23,0.04)sf(0,12,0.05) sf(1,23,0.04)
Calculates the probability of survival given a mortality table for an individual or a group.
Survival(x, n, data, prop = 1)Survival(x, n, data, prop = 1)
x |
An integer or a vector including only integers representing the age of each individual. |
n |
An integer. The term. |
data |
A data.frame of the mortality table, with the first column being the age and the second one, the probability of death. |
prop |
A numeric value. The proportion of the mortality table used, between 0 and 1. |
Survival(20,2,CSO58MANB,1) Survival(31,33,CSO80MANB,0.8)Survival(20,2,CSO58MANB,1) Survival(31,33,CSO80MANB,0.8)
Creates a mortality table under Dormoy's law.
Table_Dormoy(x0, omega, a)Table_Dormoy(x0, omega, a)
x0 |
A numeric type value. The initial age of the table. |
omega |
A numeric type value. The final age of the table. |
a |
A numeric type value. A parameter of the law. |
Returns a data.frame object containing age and death probabilities.
Chapter 3 (p 77-78) of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Table_Dormoy(0,100,0.98)Table_Dormoy(0,100,0.98)
Creates a mortality table under Gompertz's law.
Table_Gompertz(x0, omega, B, C)Table_Gompertz(x0, omega, B, C)
x0 |
A numeric type value. The initial age of the table. |
omega |
A numeric type value. The final age of the table. |
B |
A numeric type value. A parameter of the law. |
C |
A numeric type value. A parameter of the law. |
Returns a data.frame object containing age and death probabilities.
Chapter 3 (p 77-78) of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Table_Gompertz(0,100,0.00008,1.07)Table_Gompertz(0,100,0.00008,1.07)
Creates a mortality table under Makeham's law.
Table_Makeham(x0, omega, A, B, C)Table_Makeham(x0, omega, A, B, C)
x0 |
A numeric type value. The initial age of the table. |
omega |
A numeric type value. The final age of the table. |
A |
A numeric type value. A parameter of the law. |
B |
A numeric type value. A parameter of the law. |
C |
A numeric type value. A parameter of the law. |
Returns a data.frame object containing age and death probabilities.
The parameters are usually confined to the ranges shown below: 0.001 < A < 0.003, 10^(-6) < B < 10(-3), 1.08 < C < 1.12.
Chapter 3 (p 77-78) of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Table_Makeham(0,100,0.002,3*10^(-4),1.124)Table_Makeham(0,100,0.002,3*10^(-4),1.124)
Creates a mortality table under de Moivre's law.
Table_Moivre(x0, omega)Table_Moivre(x0, omega)
x0 |
A numeric type value. The initial age of the table. |
omega |
A numeric type value. The final age of the table. |
Returns a data.frame object containing age and death probabilities.
Chapter 3 (p 77-78) of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Table_Moivre(0,100)Table_Moivre(0,100)
Calculates the reserve for the life Annuity up to the moment 't'.
V_a( px, x, h, n, k = 1, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", cap, t )V_a( px, x, h, n, k = 1, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", cap, t )
px |
A numeric value. The value of the premium paid in each period. |
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of payments per year. |
cantprem |
An integer. The total number of premiums. |
premperyear |
An integer. The number of premiums to be paid per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame containing the mortality table, with the first column being the age and the second one, the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
cap |
A numeric type value. The annualized value of the payment. |
t |
An integer. The moment of valuation (in months if it is a fractional coverage or in years if it is not). |
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
V_a(147.814202915034,20,5,10,1,5,1,0.04,CSO80MANB,1,"none",100,15) V_a(148.324902023591/12,20,5,10,4,60,12,0.04,CSO80MANB,1,"constant",100,178) V_a(223633.861110949,25,0,25,12,10,1,0.04,CSO80MANB,1,"UDD",120000,300)V_a(147.814202915034,20,5,10,1,5,1,0.04,CSO80MANB,1,"none",100,15) V_a(148.324902023591/12,20,5,10,4,60,12,0.04,CSO80MANB,1,"constant",100,178) V_a(223633.861110949,25,0,25,12,10,1,0.04,CSO80MANB,1,"UDD",120000,300)
Calculates the reserve for the life insurance up to the moment 't'.
V_A.( px, x, h, n, k = 1, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", cap, t )V_A.( px, x, h, n, k = 1, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", cap, t )
px |
A numeric value. The value of the premium paid in each period. |
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of fractions per year. |
cantprem |
An integer. The total number of premiums. |
premperyear |
An integer. The number of premiums to be paid per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame containing the mortality table, with the first column being the age and the second one, the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage) |
cap |
A numeric type value. The value of the payment. |
t |
An integer. The moment of valuation (in months if it is a fractional coverage or in years if it is not). |
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
V_A.(26673.3602688847,25,2,3,1,2,1,0.04,CSO80MANB,1,"none",12000000,5) V_A.(27446.2077993839/12,25,2,3,2,24,12,0.04,CSO80MANB,1,"UDD",12000000,60) V_A.(27376.5521158244/12,25,2,3,2,24,12,0.04,CSO80MANB,1,"constant",12000000,60)V_A.(26673.3602688847,25,2,3,1,2,1,0.04,CSO80MANB,1,"none",12000000,5) V_A.(27446.2077993839/12,25,2,3,2,24,12,0.04,CSO80MANB,1,"UDD",12000000,60) V_A.(27376.5521158244/12,25,2,3,2,24,12,0.04,CSO80MANB,1,"constant",12000000,60)
Calculates the reserve for the decreasing life annuity up to the moment 't'.
V_aD( px, x, h, n, k = 1, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap, t )V_aD( px, x, h, n, k = 1, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap, t )
px |
A numeric value. The value of the premium paid in each period. |
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of payments per year. |
cantprem |
An integer. The total number of premiums. |
premperyear |
An integer. The number of premiums to be paid per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame containing the mortality table, with the first column being the age and the second one, the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
variation |
A character string. "inter" if the variation it's interannual or "intra" if it's intra-annual. |
cap |
A numeric type value. The annualized value of the first payment. |
t |
An integer. The moment of valuation (in months if it is a fractional coverage or in years if it is not). |
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
V_aD(139102.759700887,20,2,2,1,2,1,0.04,CSO80MANB,1,"none","none",100000,4) V_aD(140293.253997879/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"constant","inter",100000,48) V_aD(23461.2532906378/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"constant","intra",10000,48) V_aD(23462.5668144001/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"UDD","intra",10000,48) V_aD(14029.8183844808/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"UDD","inter",10000,48)V_aD(139102.759700887,20,2,2,1,2,1,0.04,CSO80MANB,1,"none","none",100000,4) V_aD(140293.253997879/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"constant","inter",100000,48) V_aD(23461.2532906378/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"constant","intra",10000,48) V_aD(23462.5668144001/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"UDD","intra",10000,48) V_aD(14029.8183844808/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"UDD","inter",10000,48)
Calculates the reserve for the decreasing life insurance up to the moment t.
V_AD.( px, x, h, n, k = 1, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap, t )V_AD.( px, x, h, n, k = 1, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap, t )
px |
A numeric value. The value of the premium paid in each period. |
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of fractions per year. |
cantprem |
An integer. The total number of premiums. |
premperyear |
An integer. The number of premiums to be paid per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame containing the mortality table, with the first column being the age and the second one, the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
variation |
A character string. "inter" if the variation it's inter-annual or "intra" if it's intra-annual. |
cap |
A numeric type value. Amount insured for the first year/period. |
t |
An integer. The moment of valuation (in months if it is a fractional coverage or in years if it is not). |
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
V_AD.(251.489227521537,20,2,2,1,2,1,0.04,CSO80MANB,1,"none","none",100000,4) V_AD.(432.974179723949/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"UDD","intra",100000,48) V_AD.(258.794207318685/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"UDD","inter",100000,48) V_AD.(412.784641829906/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"constant","intra",100000,48) V_AD.(258.189935788232/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"constant","inter",100000,48)V_AD.(251.489227521537,20,2,2,1,2,1,0.04,CSO80MANB,1,"none","none",100000,4) V_AD.(432.974179723949/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"UDD","intra",100000,48) V_AD.(258.794207318685/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"UDD","inter",100000,48) V_AD.(412.784641829906/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"constant","intra",100000,48) V_AD.(258.189935788232/12,20,2,2,2,24,12,0.04,CSO80MANB,1,"constant","inter",100000,48)
Calculates the reserve for the Varying Life Annuity up to the moment t.
V_av( px, x, h, n, k = 1, r, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap, t )V_av( px, x, h, n, k = 1, r, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap, t )
px |
A numeric value. The value of the premium paid in each period. |
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of payments per year. |
r |
The variation rate. A numeric type value. |
cantprem |
An integer. The total number of premiums. |
premperyear |
An integer. The number of premiums to be paid per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame containing the mortality table, with the first column being the age and the second one, the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
variation |
A character string. "inter" if the variation it's interannual or "intra" if it's intra-annual. |
cap |
A numeric type value. The annualized value of the first payment. |
t |
An integer. The moment of valuation (in months if it is a fractional coverage or in years if it is not). |
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
V_av(9435943.49607651,20,2,2,1,0.05,2,1,0.04,CSO80MANB,1,"none","none",10000000,4) V_av(9516712.17583443/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","inter",10000000,48) V_av(9517.04683383614/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","inter",10000,48) V_av(997.404109454868/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","intra",1000,48) V_av(997436.738989113/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","intra",1000000,48) V_av(28.4421691213902,40,3,7,2,0.7,1,1,0.04,CSO80MANB,1,"UDD","intra",1,120)V_av(9435943.49607651,20,2,2,1,0.05,2,1,0.04,CSO80MANB,1,"none","none",10000000,4) V_av(9516712.17583443/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","inter",10000000,48) V_av(9517.04683383614/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","inter",10000,48) V_av(997.404109454868/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","intra",1000,48) V_av(997436.738989113/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","intra",1000000,48) V_av(28.4421691213902,40,3,7,2,0.7,1,1,0.04,CSO80MANB,1,"UDD","intra",1,120)
Calculates the reserve for the varying life insurance up to the moment t.
V_Av.( px, x, h, n, k = 1, r, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap, t )V_Av.( px, x, h, n, k = 1, r, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap, t )
px |
A numeric value. The value of the premium paid in each period. |
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of fractions per year. |
r |
The variation rate. A numeric type value. |
cantprem |
An integer. The total number of premiums. |
premperyear |
An integer. The number of premiums to be paid per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame containing the mortality table, with the first column being the age and the second one, the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
variation |
A character string. "inter" if the variation it's interannual or "intra" if it's intra-annual. |
cap |
A numeric type value. Amount insured for the first year/period. |
t |
An integer. The moment of valuation (in months if it is a fractional coverage or in years if it is not). |
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
V_Av.(333.373580168544,20,2,2,1,0.05,1,1,0.04,CSO80MANB,1,"none","none",100000,4) V_Av.(175.054867728107/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","inter",100000,48) V_Av.(183.436285298212/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","intra",100000,48) V_Av.(183.965812992762/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","intra",100000,48) V_Av.(174.645127871177/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","inter",100000,48)V_Av.(333.373580168544,20,2,2,1,0.05,1,1,0.04,CSO80MANB,1,"none","none",100000,4) V_Av.(175.054867728107/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","inter",100000,48) V_Av.(183.436285298212/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","intra",100000,48) V_Av.(183.965812992762/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","intra",100000,48) V_Av.(174.645127871177/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","inter",100000,48)
Calculates the reserve for the Varying Life Annuity up to the moment t.
V_avg( px, x, h, n, k = 1, r, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap, t )V_avg( px, x, h, n, k = 1, r, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap, t )
px |
A numeric value. The value of the premium paid in each period. |
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of payments per year. |
r |
The variation rate. A numeric type value. |
cantprem |
An integer. The total number of premiums. |
premperyear |
An integer. The number of premiums to be paid per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame containing the mortality table, with the first column being the age and the second one, the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
variation |
A character string. "inter" if the variation it's interannual or "intra" if it's intra-annual. |
cap |
A numeric type value. The annualized value of the first payment. |
t |
An integer. The moment of valuation (in months if it is a fractional coverage or in years if it is not). |
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
V_avg(94359.4349607651,20,2,2,1,0.05,2,1,0.04,CSO80MANB,1,"none","none",100000,4) V_avg(95167.1217583443/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","inter",100000,48) V_avg(99969.5282890978/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","intra",100000,48) V_avg(95170.4683383614/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","inter",100000,48) V_avg(99972.7870462341/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","intra",100000,48)V_avg(94359.4349607651,20,2,2,1,0.05,2,1,0.04,CSO80MANB,1,"none","none",100000,4) V_avg(95167.1217583443/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","inter",100000,48) V_avg(99969.5282890978/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","intra",100000,48) V_avg(95170.4683383614/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","inter",100000,48) V_avg(99972.7870462341/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","intra",100000,48)
Calculates the reserve for the varying life insurance up to the moment t.
V_Avg.( px, x, h, n, k = 1, r, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap, t )V_Avg.( px, x, h, n, k = 1, r, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", variation = "none", cap, t )
px |
A numeric value. The value of the premium paid in each period. |
x |
An integer. The age of the insuree. |
h |
An integer. The deferral period. |
n |
An integer. Number of years of coverage. |
k |
An integer. Number of fractions per year. |
r |
The variation rate. A numeric type value. |
cantprem |
An integer. The total number of premiums. |
premperyear |
An integer. The number of premiums to be paid per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame containing the mortality table, with the first column being the age and the second one, the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
variation |
A character string. "inter" if the variation it's interannual or "intra" if it's intra-annual. |
cap |
A numeric type value. Amount insured for the first year/period. |
t |
An integer. The moment of valuation (in months if it is a fractional coverage or in years if it is not). |
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
V_Avg.(170.113596880528,20,2,2,1,0.05,2,1,0.04,CSO80MANB,1,"none","none",100000,4) V_Avg.(183.854458536232/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","intra",100000,48) V_Avg.( 175.054867728107/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","inter",100000,48) V_Avg.(184.431102889578/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","intra",100000,48) V_Avg.(174.645127871158/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","inter",100000,48)V_Avg.(170.113596880528,20,2,2,1,0.05,2,1,0.04,CSO80MANB,1,"none","none",100000,4) V_Avg.(183.854458536232/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","intra",100000,48) V_Avg.( 175.054867728107/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"UDD","inter",100000,48) V_Avg.(184.431102889578/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","intra",100000,48) V_Avg.(174.645127871158/12,20,2,2,2,0.05,24,12,0.04,CSO80MANB,1,"constant","inter",100000,48)
Calculates the reserve for the Pure endowments up to the moment t.
V_E( px, x, n, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", cap, t )V_E( px, x, n, cantprem = 1, premperyear = 1, i = 0.04, data, prop = 1, assumption = "none", cap, t )
px |
A numeric value. The value of the premium paid in each period. |
x |
An integer. The age of the insuree. |
n |
The term of the endowment. An integer, for annual coverage, or a numeric for fractional coverage. |
cantprem |
An integer. The total number of premiums. |
premperyear |
An integer. The number of premiums to be paid per year. |
i |
The interest rate. A numeric type value. |
data |
A data.frame containing the mortality table, with the first column being the age and the second one, the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table used (between 0 and 1). |
assumption |
A character string. The assumption used for fractional ages ("UDD" for uniform distribution of deaths, "constant" for constant force of mortality and "none" if there is no fractional coverage). |
cap |
A numeric type value. The payment. |
t |
An integer. The moment of valuation (in months if it is a fractional coverage or in years if it is not). |
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
V_E(663.501989747591,20,10,1,1,0.04,CSO80MANB,1,"none",1000,10) V_E(9383.64446819386/12,20,2,12,12,0.04,CSO80MANB,1,"constant",10000,24) V_E(9383.64446819386/12,20,2,12,12,0.04,CSO80MANB,1,"constant",10000,24)V_E(663.501989747591,20,10,1,1,0.04,CSO80MANB,1,"none",1000,10) V_E(9383.64446819386/12,20,2,12,12,0.04,CSO80MANB,1,"constant",10000,24) V_E(9383.64446819386/12,20,2,12,12,0.04,CSO80MANB,1,"constant",10000,24)
Calculates the reserve for the loan insurance up to the moment t.
V_Payment_Protection( px, x, n, k = 1, cantprem = 1, premperyear = 1, i = 0.04, ip = 0.04, data, prop = 1, type = "outstanding_debt", method = "interest_only", V0, t )V_Payment_Protection( px, x, n, k = 1, cantprem = 1, premperyear = 1, i = 0.04, ip = 0.04, data, prop = 1, type = "outstanding_debt", method = "interest_only", V0, t )
px |
A numeric value. The value of the premium paid in each period. |
x |
An integer. The age of the insuree. |
n |
An integer. Loan term (in years). |
k |
An integer. Number of payments per year. |
cantprem |
An integer. The total number of premiums. |
premperyear |
An integer. The number of premiums to be paid per year. |
i |
The interest rate. A numeric type value. |
ip |
The interest rate of the loan. A numeric type value. |
data |
A data.frame of the mortality table, with the first column being the age and the second one the probability of death. |
prop |
A numeric value. It represents the proportion of the mortality table used (between 0 and 1). |
type |
A character string. The type of loan protection/reimburstment ("outstanding_debt" or "payments"). |
method |
A character string. Amortization scheme ("constant_instalment", "interest_only" or "constant_principal"). |
V0 |
A numeric type value. Loan value. |
t |
An integer. The moment of valuation (in months if it is a fractional coverage or in years if it is not). |
Returns the actuarial present value of the loan protection.
px1<-31.6216618772779 c1<-10500 V_Payment_Protection(px1,30,25,1,10,1,0.06,0.07,CSO80FANB,1,"payments","constant_instalment",c1,25)px1<-31.6216618772779 c1<-10500 V_Payment_Protection(px1,30,25,1,10,1,0.06,0.07,CSO80FANB,1,"payments","constant_instalment",c1,25)