# V_Av.: Reserve Valuation for Varying Life Insurance: Arithmetic... In DetLifeInsurance: Life Insurance Premium and Reserves Valuation

## Description

Calculates the reserve for the varying life insurance up to the moment t.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```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

 ```1 2 3 4 5``` ```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) ```

DetLifeInsurance documentation built on July 8, 2020, 7 p.m.