# V_aD: Reserve Valuation for Decreasing life annuities In DetLifeInsurance: Life Insurance Premium and Reserves Valuation

## Description

Calculates the reserve for the decreasing life annuity up to the moment 't'.

## Usage

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

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

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