# axn_1: Function to evaluate life insurance. In spedygiorgio/lifecontingencies: Financial and Actuarial Mathematics for Life Contingencies

## Description

This function evaluates n - years term and whole life insurance.

## Usage

 ```1 2``` ```Axn(actuarialtable, x, n, i=actuarialtable@interest, m, k=1, type = "EV", power=1, ...) ```

## Arguments

 `actuarialtable` An actuarial table object. `x` Age of the insured. (can be a vector). `n` Coverage period, if missing the insurance is considered whole life n=ω-x-m. (can be a vector). `i` Interest rate (overrides the interest rate slot in `actuarialtable`). (should be a scalar). `m` Deferring period, even fractional, if missing assumed to be 0. (can be a vector). `k` Number of periods per year at the end of which the capital is payable in case of insured event, default=1 (capital payable at the end of death year). (should be a scalar). `type` A string, either `"EV"` for expected value of the actuarial present value (default) or `"ST"` for one stochastic realization of the underlying present value of benefits. Alternatively, one can use `"expected"` or `"stochastic"` respectively (can be abbreviated). `power` The power of the APV. Default is 1 (mean) `...` Arguments to be passed to `pxt()`.

## Details

The variance calculation has not been implemented yet.

## Value

A numeric value representing either the actuarial value of the coverage (when type="EV") or a number drawn from the underlying distribution of Axn.

## Warning

The function is provided as is, without any guarantee regarding the accuracy of calculation. We disclaim any liability for eventual losses arising from direct or indirect use of this software.

## Note

It is possible that value returned by stochastic simulation are biased. Successive releases of this software will analyze the issue with detail.

## Author(s)

Giorgio A. Spedicato

## References

Actuarial Mathematics (Second Edition), 1997, by Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J.

`axn`, `Exn`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ``` #assume SOA example life table to be load data(soaLt) soa08Act=with(soaLt, new("actuarialtable",interest=0.06, x=x,lx=Ix,name="SOA2008")) #evaluate the value of a 40 years term life insurance for an aged 25 Axn(actuarialtable=soa08Act, x=25, n=40) #check an relevant life contingencies relationship k=12 i=0.06 j=real2Nominal(i,k) Axn(soa08Act, 30,k=12) i/j*Axn(soa08Act, 30,k=1) ```