| Type: | Package |
| Title: | Life Insurance Premium and Reserves Valuation |
| Version: | 0.1.3 |
| Maintainer: | Joaquin Auza <auzajoaquin@gmail.com> |
| 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. |
| License: | GPL-3 |
| Depends: | R (≥ 3.5.0) |
| Imports: | utils |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.1.0 |
| URL: | https://github.com/JoaquinAuza/DetLifeInsurance |
| BugReports: | https://github.com/JoaquinAuza/DetLifeInsurance/issues |
| VignetteBuilder: | knitr |
| Suggests: | knitr, rmarkdown |
| NeedsCompilation: | no |
| Packaged: | 2020-09-12 09:03:15 UTC; citio |
| Author: | Joaquin Auza [aut, cre], Maria Sol Alvarez [aut] |
| Repository: | CRAN |
| Date/Publication: | 2020-09-12 09:20:07 UTC |
Life Insurance
Description
Calculates the present value of the life insurance.
Usage
A.(x, h, n, k = 1, i = 0.04, data, prop = 1, assumption = "none", cap = 1)
Arguments
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. |
Value
Returns a numeric value (actuarial present value).
References
Chapter 3 of Life Contingencies (1952) by Jordan, chapter 4 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Examples
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)
Continuous Life Insurance
Description
Calculates the present value of a continuous life insurance.
Usage
ACont.(x, h, n, i = 0.04, data, prop = 1, assumption = "UDD", cap = 1)
Arguments
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. |
Value
Returns a numeric (actuarial present value).
References
Chapter 3 of Life Contingencies (1952) by Jordan, chapter 4 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Examples
ACont.(24,2,10,0.04,CSO80MANB,1,"UDD",1)
ACont.(24,2,10,0.04,CSO80MANB,1,"constant",1)
Decreasing Life Insurance
Description
Calculates the present value of a decreasing life insurance.
Usage
AD.(
x,
h,
n,
k = 1,
i = 0.04,
data,
prop = 1,
assumption = "none",
variation = "none",
cap = 1
)
Arguments
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. |
Value
Returns a numeric value (actuarial present value).
References
Chapter 3 of Life Contingencies (1952) by Jordan, chapter 4 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Examples
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)
Life Insurance of a group
Description
Calculates the present value of a life insurance coverage for a group.
Usage
Am.(
x,
h,
n,
k = 1,
i = 0.04,
data,
prop = 1,
ndeath = 1,
assumption = "none",
cap = 1
)
Arguments
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. |
Value
Returns a numeric value (actuarial present value).
Examples
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)
ArgentinaINDEC9092 Female
Description
Mortality table (ultimate): Argentina Instituto Nacional de Estadistica y Censos (INDEC). Nation: Argentina. Year: 1990-1992. Sex: Female.
Usage
data(ArgentinaINDEC9092F)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20002
ArgentinaINDEC9092 Male
Description
Mortality table (ultimate): Argentina Instituto Nacional de Estadistica y Censos (INDEC). Nation: Argentina. Year: 1990-1992. Sex: Male.
Usage
data(ArgentinaINDEC9092M)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20001
ArgentinaINDEC9092 Males and Females Combined
Description
Mortality table (ultimate): Argentina Instituto Nacional de Estadistica y Censos (INDEC). Nation: Argentina. Year: 1990-1992. Sex: Males and Females Combined.
Usage
data(ArgentinaINDEC9092comb)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20003
Varying Life Insurance: Arithmetic Progression
Description
Calculates the present value of a varying life insurance according to a arithmetic progression.
Usage
Av.(
x,
h,
n,
k = 1,
r = 1,
i = 0.04,
data,
prop = 1,
assumption = "none",
variation = "none",
cap = 1
)
Arguments
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. |
Value
Returns a numeric value (actuarial present value).
Note
For an increasing life insurance coverage, 'r' must be 1.
References
Chapter 4 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Examples
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)
Varying Life Insurance: Geometric Progression
Description
Calculates the present value of a varying life insurance according to a geometric progression.
Usage
Avg.(
x,
h,
n,
k = 1,
r,
i = 0.04,
data,
prop = 1,
assumption = "none",
variation = "none",
cap = 1
)
Arguments
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. |
Value
Returns a numeric value (actuarial present value).
References
Chapter 4 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Examples
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)
CSO2001 Female Age Last Birthday Non-smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Female. Basis: Age Last Birthday. Smoker: No.
Usage
data(CSO2001FALBnonsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1517
CSO2001 Female Age Last Birthday Smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Female. Basis: Age Last Birthday. Smoker: yes.
Usage
data(CSO2001FALBsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1519
CSO2001 Female Age Nearest Birthday Non-smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Female. Basis: Age Nearest Birthday. Smoker: No.
Usage
data(CSO2001FANBnonsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1140
CSO2001 Female Age Nearest Birthday Smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Female. Basis: Age Nearest Birthday. Smoker: Yes.
Usage
data(CSO2001FANBsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1141
CSO2001 Male Age Last Birthday Non-smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Male. Basis: Age Last Birthday. Smoker: No.
Usage
data(CSO2001MALBnonsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1516
CSO2001 Male Age Last Birthday Smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Male. Basis: Age Last Birthday. Smoker: yes.
Usage
data(CSO2001MALBsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1518
CSO2001 Male Age Nearest Birthday Non-smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Male. Basis: Age Nearest Birthday. Smoker: No.
Usage
data(CSO2001MANBnonsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1137
CSO2001 Male Age Nearest Birthday Smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 2001. Sex: Male. Basis: Age Nearest Birthday. Smoker: Yes.
Usage
data(CSO2001MANBsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1138
CSO58 Female Age Last Birthday
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Year: 1958. Nation: United States of America. Sex: Female. Basis: Age Last Birthday.
Usage
data(CSO58FALB)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=8
CSO58 Female Age Nearest Birthday
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1958. Sex: Female. Basis: Age Nearest Birthday.
Usage
data(CSO58FANB)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=6
CSO58 Male Age Last Birthday
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1958. Sex: Male. Basis: Age Last Birthday.
Usage
data(CSO58MALB)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=7
CSO58 Male Age Nearest Birthday
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1958. Sex: Male. Basis: Age Nearest Birthday.
Usage
data(CSO58MANB)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=5
CSO80 Female Age Last Birthday
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Female Age method: Age Last Birthday.
Usage
data(CSO80FALB)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=35
CSO80 Female Age Last Birthday non-smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Female. Basis: Age Last Birthday. Smoker: No.
Usage
data(CSO80FALBnonsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=37
CSO80 Female Age Last Birthday smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Female. Basis: Age Last Birthday. Smoker: Yes.
Usage
data(CSO80FALBsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=39
CSO80 Female Age Nearest Birthday
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Female. Basis: Age Nearest Birthday.
Usage
data(CSO80FANB)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=36
CSO80 Female Age Nearest Birthday Non-smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Female. Basis: Age Nearest Birthday. Smoker: No.
Usage
data(CSO80FANBnonsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=38
CSO80 Female Age Nearest Birthday Smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Female. Basis: Age Nearest Birthday. Smoker: Yes.
Usage
data(CSO80FANBsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=40
CSO80 Male Age Last Birthday
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Male. Basis: Age Last Birthday.
Usage
data(CSO80MALB)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=41
CSO80 Male Age Last Birthday Non-smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Male. Basis: Age Last Birthday. Smoker: No.
Usage
data(CSO80MALBnonsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=43
CSO80 Male Age Last Birthday Smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Male. Basis: Age Last Birthday. Smoker: Yes.
Usage
data(CSO80MALBsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=45
CSO80 Male Age Nearest Birthday
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Male. Age method: Age Nearest Birthday.
Usage
data(CSO80MANB)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=42
CSO80 Male Age Nearest Birthday Non-smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Male. Basis: Age Nearest Birthday. Smoker: No.
Usage
data(CSO80MANBnonsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=44
CSO80 Male Age Nearest Birthday Smoker
Description
Mortality table (ultimate): Commissioner's Standard Ordinary. Nation: United States of America. Year: 1980. Sex: Male. Basis: Age Nearest Birthday. Smoker: Yes.
Usage
data(CSO80MANBsmoker)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=46
Pure Endowment
Description
Calculates the Pure endowments.
Usage
E(x, n, i = 0.04, data, prop = 1, assumption = "none", cap = 1)
Arguments
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. |
References
Chapter 2 of Life Contingencies (1952) by Jordan.
Examples
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)
Group Pure Endowment
Description
Calculates the Pure endowments for a group of insurees.
Usage
Em(
x,
n,
i = 0.04,
data,
prop = 1,
type = "joint",
quant = 1,
assumption = "none",
cap = 1
)
Arguments
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. |
Examples
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)
Fractional table of mortality
Description
Creates a fractional mortality table for a given mortality table.
Usage
Fractional_table(data, frac, i = 0.04, assumption = "UDD")
Arguments
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). |
Value
Returns a data.frame object containing fractional age and death probability vectors.
References
Chapter 3 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt
Examples
Fractional_table(CSO80MANB,2,0.04,"constant")
Fractional_table(CSO80MANB,2,0.04,"UDD")
GAM71 Female
Description
Mortality table (ultimate): Group Annuity Mortality. Nation: United States of America. Year: 1971. Sex: Female.
Usage
data(GAM71F)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=817, http://servicios.infoleg.gob.ar/infolegInternet/anexos/80000-84999/81029/norma.htm
GAM71 Male
Description
Mortality table (ultimate): Group Annuity Mortality. Nation: United States of America. Year: 1971. Sex: Male.
Usage
data(GAM71M)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=818, http://servicios.infoleg.gob.ar/infolegInternet/anexos/80000-84999/81029/norma.htm
GAM83 Female
Description
Mortality table (ultimate): Group Annuity Mortality. Nation: United States of America. Year: 1983. Sex: Female.
Usage
data(GAM83F)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=825
GAM83 Male
Description
Mortality table (ultimate): Group Annuity Mortality. Nation: United States of America. Year: 1983. Sex: Male.
Usage
data(GAM83M)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=826
GAM94 Female
Description
Mortality table (ultimate): Group Annuity Mortality. Year: 1994. Sex: Female.
Usage
data(GAM94F)
Format
a dataframe containing a column for age (x) and a column for death probability (q)
References
GAM94 Female Age Nearest Birthday
Description
Mortality table (ultimate): Group Annuity Mortality. Nation: United States of America. Year: 1994. Sex: Female. Basis: Age Nearest Birthday.
Usage
data(GAM94FANB)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=834
GAM94 Male
Description
Mortality table (ultimate): Group Annuity Mortality. Year: 1994. Sex: Male.
Usage
data(GAM94M)
Format
a dataframe containing a column for age (x) and a column for death probability (q)
References
GAM94 Male Age Nearest Birthday
Description
Mortality table (ultimate): Group Annuity Mortality. Nation: United States of America. Year: 1994. Sex: Male. Basis: Age Nearest Birthday.
Usage
data(GAM94MANB)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=835
Joint Survival Probability
Description
Calculates the probability of survival given a mortality table for a group.
Usage
JointSurvival(x, n, data, prop = 1)
Arguments
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. |
Examples
ages<-c(34,45,52,65)
JointSurvival(ages,10,CSO80FALB)
Loan Amortization
Description
Calculates the amortization schedule.
Usage
Loan_amortization(V0, n, i, i2 = 0, alic = 0, ins = 0, method)
Arguments
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" ). |
Value
Returns a data.frame object containing Period, Payment, Pure Payment, Intrest, Amortization, Insurance, TAX and Outstanding debt.
Examples
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")
MAyP0206 Combined Active and Retired Female
Description
Mortality table (ultimate): Mortalidad Activos y Pasivos. Nation: Argentina. Year: 2002-2006. Sex: Female. Status: Combined Active and Retired.
Usage
data(MAyP0206CAF)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20009
MAyP0206 Combined Active and Retired Male
Description
Mortality table (ultimate): Mortalidad Activos y Pasivos. Nation: Argentina. Year: 2002-2006. Sex: Male. Status: Combined Active and Retired.
Usage
data(MAyP0206CAM)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20008
MAyP0206 Active Female
Description
Mortality table (ultimate): Mortalidad Activos y Pasivos. Nation: Argentina. Year: 2002-2006. Sex: Female. Status: Active.
Usage
data(MAyP0206activeF)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20005
MAyP0206 Active Male
Description
Mortality table (ultimate): Mortalidad Activos y Pasivos. Nation: Argentina. Year: 2002-2006. Sex: Male. Status: Active.
Usage
data(MAyP0206activeM)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20004
MAyP0206 Retired Female
Description
Mortality table (ultimate): Mortalidad Activos y Pasivos. Nation: Argentina. Year: 2002-2006. Sex: Female. Status: Retired.
Usage
data(MAyP0206retiredF)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20007
MAyP0206 Retired Male
Description
Mortality table (ultimate): Mortalidad Activos y Pasivos. Nation: Argentina. Year: 2002-2006. Sex: Male. Status: Retired.
Usage
data(MAyP0206retiredM)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=20006
Mi06 Female
Description
Mortality table (ultimate): Mortalidad Invalidez. Nation: Chile. Year: 2006. Sex: Female.
Usage
data(Mi06F)
Format
A data frame containing a column for age (x) and a column for death probability (q).
Note
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
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=2713,https://www.spensiones.cl/portal/compendio/596/w3-propertyvalue-3542.html
Mi06 Male
Description
Mortality table (ultimate): Mortalidad Invalidez. Nation: Chile. Year: 2006. Sex: Male.
Usage
data(Mi06M)
Format
A data frame containing a column for age (x) and a column for death probability (q).
Note
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
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=2712,https://www.spensiones.cl/portal/compendio/596/w3-propertyvalue-3542.html
Mi85 Female
Description
Mortality table (ultimate): Mortalidad Invalidez. Nation: Chile. Year: 1985. Sex: Female.
Usage
data(Mi85F)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
http://servicios.infoleg.gob.ar/infolegInternet/anexos/80000-84999/81029/norma.htm
Mi85 Male
Description
Mortality table (ultimate): Mortalidad Invalidez. Nation: Chile. Year: 1985. Sex: Male.
Usage
data(Mi85M)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
http://servicios.infoleg.gob.ar/infolegInternet/anexos/80000-84999/81029/norma.htm
Payment Protection
Description
Calculates the present value of the loan insurance.
Usage
Payment_Protection(
x,
n,
k = 1,
V0,
i = 0.04,
ip = 0.04,
data,
prop = 1,
type = "outstanding_debt",
method = "interest_only"
)
Arguments
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"). |
Value
Returns a numeric value (actuarial present value).
Examples
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")
Fractional Premium
Description
Calculates the annualized value of the fractional premiums.
Usage
PremiumFrac(px1, x, m, k, i = 0.04, data, prop = 1, effect = "yes", assumption)
Arguments
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). |
Value
Returns the annualized value of the fractional premium.
Note
If k=1, regardless of the "effect", the returned value is the annual premium.
References
Chapter 4 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters
Examples
PremiumFrac(1000,20,10,2,0.04,CSO80MANB,1,"yes","constant")
PremiumFrac(1000,20,10,2,0.04,CSO80MANB,1,"no","UDD")
RV04 Female
Description
Mortality table (ultimate): Renta Vitalicia. Nation: Chile. Year: 2004. Sex: Female.
Usage
data(RV04F)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1500
RV04 Male
Description
Mortality table (ultimate): Renta Vitalicia. Nation: Chile. Year: 2004. Sex: Male.
Usage
data(RV04M)
Format
A data frame containing a column for age (x) and a column for death probability (q).
References
https://mort.soa.org/ViewTable.aspx?&TableIdentity=1499
Interest & Discount Rate Converter
Description
Converts nominal and effective interest and discount rates.
Usage
Rate_converter(num, rate1, m, rate2, k, type = "days")
Arguments
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"). |
Examples
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")
Survival Probability
Description
Calculates the probability of survival given a mortality table for an individual or a group.
Usage
Survival(x, n, data, prop = 1)
Arguments
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. |
Examples
Survival(20,2,CSO58MANB,1)
Survival(31,33,CSO80MANB,0.8)
Dormoy's Law of Mortality Table Creator
Description
Creates a mortality table under Dormoy's law.
Usage
Table_Dormoy(x0, omega, a)
Arguments
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. |
Value
Returns a data.frame object containing age and death probabilities.
References
Chapter 3 (p 77-78) of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Examples
Table_Dormoy(0,100,0.98)
Gompertz's Law of Mortality Table Creator
Description
Creates a mortality table under Gompertz's law.
Usage
Table_Gompertz(x0, omega, B, C)
Arguments
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. |
Value
Returns a data.frame object containing age and death probabilities.
References
Chapter 3 (p 77-78) of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Examples
Table_Gompertz(0,100,0.00008,1.07)
Makeham's Law of Mortality Table Creator
Description
Creates a mortality table under Makeham's law.
Usage
Table_Makeham(x0, omega, A, B, C)
Arguments
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. |
Value
Returns a data.frame object containing age and death probabilities.
Note
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.
References
Chapter 3 (p 77-78) of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Examples
Table_Makeham(0,100,0.002,3*10^(-4),1.124)
de Moivre's Law of Mortality Table Creator
Description
Creates a mortality table under de Moivre's law.
Usage
Table_Moivre(x0, omega)
Arguments
x0 |
A numeric type value. The initial age of the table. |
omega |
A numeric type value. The final age of the table. |
Value
Returns a data.frame object containing age and death probabilities.
References
Chapter 3 (p 77-78) of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Examples
Table_Moivre(0,100)
Reserve for Life Insurance
Description
Calculates the reserve for the life insurance up to the moment 't'.
Usage
V_A.(
px,
x,
h,
n,
k = 1,
cantprem = 1,
premperyear = 1,
i = 0.04,
data,
prop = 1,
assumption = "none",
cap,
t
)
Arguments
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). |
Value
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
References
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Examples
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)
Reserve Valuation for Decreasing Life Insurance
Description
Calculates the reserve for the decreasing life insurance up to the moment t.
Usage
V_AD.(
px,
x,
h,
n,
k = 1,
cantprem = 1,
premperyear = 1,
i = 0.04,
data,
prop = 1,
assumption = "none",
variation = "none",
cap,
t
)
Arguments
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). |
Value
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
References
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Examples
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)
Reserve Valuation for Varying Life Insurance: Arithmetic Progression
Description
Calculates the reserve for the varying life insurance up to the moment t.
Usage
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
)
Arguments
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). |
Value
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
References
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Examples
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)
Reserve Valuation for Varying Life Insurance: Geometric Progression
Description
Calculates the reserve for the varying life insurance up to the moment t.
Usage
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
)
Arguments
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). |
Value
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
References
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Examples
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)
Reserve Valuation for Pure Endowments
Description
Calculates the reserve for the Pure endowments up to the moment t.
Usage
V_E(
px,
x,
n,
cantprem = 1,
premperyear = 1,
i = 0.04,
data,
prop = 1,
assumption = "none",
cap,
t
)
Arguments
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). |
Value
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
References
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Examples
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)
Reserve valuation for Payment Protection
Description
Calculates the reserve for the loan insurance up to the moment t.
Usage
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
)
Arguments
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). |
Value
Returns the actuarial present value of the loan protection.
Examples
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)
Reserve Valuation for Life Annuities
Description
Calculates the reserve for the life Annuity up to the moment 't'.
Usage
V_a(
px,
x,
h,
n,
k = 1,
cantprem = 1,
premperyear = 1,
i = 0.04,
data,
prop = 1,
assumption = "none",
cap,
t
)
Arguments
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). |
Value
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
References
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Examples
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)
Reserve Valuation for Decreasing life annuities
Description
Calculates the reserve for the decreasing life annuity up to the moment 't'.
Usage
V_aD(
px,
x,
h,
n,
k = 1,
cantprem = 1,
premperyear = 1,
i = 0.04,
data,
prop = 1,
assumption = "none",
variation = "none",
cap,
t
)
Arguments
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). |
Value
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
References
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Examples
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)
Reserve Valuation for Varying Life Annuities: Arithmetic Progression
Description
Calculates the reserve for the Varying Life Annuity up to the moment t.
Usage
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
)
Arguments
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). |
Value
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
References
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Examples
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)
Reserve Valuation for Varying Life Annuities: Geometric Progression
Description
Calculates the reserve for the Varying Life Annuity up to the moment t.
Usage
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
)
Arguments
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). |
Value
A data frame with Premium, Risk, 1/E and reserve values up to the moment t.
References
Chapter 5 of Life Contingencies (1952) by Jordan, Chapter 11 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Examples
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)
Life Annuities
Description
Calculates the present value of a life annuity.
Usage
a(x, h, n, k = 1, i = 0.04, data, prop = 1, assumption = "none", cap = 1)
Arguments
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. |
Value
Returns a numeric value (actuarial present value).
References
Chapter 2 of Life Contingencies (1952) by Jordan, chapter 5 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Examples
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)
Continuous Life Annuities
Description
Calculates the present value of a continuous life annuity.
Usage
aCont(x, h, n, i = 0.04, data, prop = 1, assumption = "constant", cap = 1)
Arguments
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. |
Value
Returns a numeric value (the actuarial present value).
References
Chapter 2 of Life Contingencies (1952) by Jordan, chapter 5 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Examples
aCont(35,7,10,0.04,CSO80MANB,1,"constant",1)
aCont(23,5,12,0.04,CSO80MANB,1,"UDD",1)
Decreasing Life Annuities
Description
Calculates the present value of a decreasing life annuity.
Usage
aD(
x,
h,
n,
k = 1,
i = 0.04,
data,
prop = 1,
assumption = "none",
variation = "none",
cap = 1
)
Arguments
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. |
Value
Returns a numeric value (actuarial present value).
References
Chapter 2 of Life Contingencies (1952) by Jordan, chapter 5 of Actuarial Mathematics (1997) by Bowers, Gerber, Hickman, Jones & Nesbitt.
Examples
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)
Present Value of An Annuity
Description
Calculates the present value of an annuity.
Usage
af(l = 0, n, i)
Arguments
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. |
Examples
af(0,10,0.03)
af(1,15,0.05)
Life Annuities for a group
Description
Calculates the present value of a life annuity for a group.
Usage
am(
x,
h,
n,
k = 1,
i = 0.04,
data,
prop = 1,
type = "joint",
quant = 1,
assumption = "none",
cap = 1
)
Arguments
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. |
Value
Returns a numeric value (actuarial present value).
Examples
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")
Varying Life Annuities: Arithmetic Progression
Description
Calculates the present value of a varying life annuity according to a arithmetic progression.
Usage
av(
x,
h,
n,
k = 1,
r = 1,
i = 0.04,
data,
prop = 1,
assumption = "none",
variation = "none",
cap = 1
)
Arguments
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. |
Value
Returns a numeric value (actuarial present value).
Note
For an increasing life annuity coverage, 'r' must be 1.
References
Chapter 5 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Examples
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)
Varying Life Annuities: Geometric Progression
Description
Calculates the present value of a varying life annuity according to a geometric progression.
Usage
avg(
x,
h,
n,
k = 1,
r,
i = 0.04,
data,
prop = 1,
assumption = "none",
variation = "none",
cap = 1
)
Arguments
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. |
Value
Returns a numeric value (actuarial present value).
References
Chapter 5 of Actuarial Mathematics for Life Contingent Risks (2009) by Dickson, Hardy and Waters.
Examples
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)
Fractional Probability of Death
Description
Calculates the fractional probability for a person of x+s/k dies before age x+(s+1)/k.
Usage
qfrac(x, s, k, i, data, assumption, prop)
Arguments
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). |
Value
The fractional probability of death.
Examples
qfrac(27,1,4,0.04,CSO80MANB,"constant",1)
qfrac(20,0,12,0.04,CSO80MANB,"UDD",0.8)
Future Value of an Annuity
Description
Calculates the future value of an annuity.
Usage
sf(l = 0, n, i)
Arguments
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. |
Examples
sf(0,12,0.05)
sf(1,23,0.04)