Life Insurance Premium and Reserves Valuation

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) and "Life Contingencies" by Jordan, C. W (1952) . It also contains functions for equivalent interest and discount rate calculation, present and future values of annuities, and loan amortization schedule.

DetLifeInsurance

DetLifeInsurance is an R package designed to provide tools for:

• Deterministic valuation of actuarial reserves and life insurance and annuities premiums (both constant and variable amounts supported).
• Applying fractional age assumptions to life tables, and generating new ones based on mortality laws.
• Calculation of equivalent interest-discount rates as well as future and present value of annuities.
• Calculation of loan amortization schedule.

In addition, 47 commonly used mortality tables are included as data.

Installation

To install from CRAN, use:

install.packages("DetLifeInsurance")

To install from GitHub, use:

#library(devtools)
devtools::install_github("JoaquinAuza/DetLifeInsurance")

Note: package devtools must be installed.

Example #1

In this example, we obtain the annual net premium of a life insurance coverage of $100000 for a term of 5 years, issued to a male of age 30, using an interest rate of 3.5%.

#library(DetLifeInsurance)

LI <- A.(x=30, h=0, n=5, i = 0.035, data=CSO80MANB, cap = 100000) #Actuarial PV of the LI
Prem <- a(x=30, h=0, n=5, k=1, i=0.035, data=CSO80MANB , assumption="UDD")
Net_Premium <- LI/Prem #Net premium to be paid at the begining of each year

#The same result can be achieved by using PremiumFrac()

Net_Premium <-PremiumFrac(px1=LI, x=30,m=5,i=0.035,k=1,data=CSO80MANB)

Example #2

In this example, we obtain the value of the actuarial reserve for a life insurance coverage where the insuree pays monthly premiums during the first year. UDD assumption is used.

#library(DetLifeInsurance)

LI <- A.(x=30, h=0, n=5, i = 0.035, data=CSO80MANB, cap = 100000) 

Net_Premium <- PremiumFrac(px1=LI,x=30,m=1,k=12,i=0.035,data= CSO80MANB,assumption = "UDD")
Net_Premium_monthly <- Net_Premium/12

V_A.(px=Net_Premium_monthly, x=30, h=0, n=5, k = 1, cantprem = 12,
     premperyear = 12, i = 0.035, data=CSO80MANB, assumption = "UDD", 
     cap=100000, t=60)

Status

Work in progress!

• [x] Basic functionality.
• [x] Enhanced documentation.
• [x] Fix references, fix non-exporable functions.
• [x] Upload to CRAN.
• [x] New functions: group insurance, loan insurance reserves...
• [ ] what else?