endowsingle: Single endowment insurance product

In nathanesau/stocins: Stochastic Interest Rate Models for Life Insurance

Description

An endowment insurance pays a benefit of d if the policyholder dies within the term of the contract and e if the policyholder survives the term of the contract.

In addition to the functions described in the insurance class, other functions are available for the endowsingle class.

In particular, z.ev.two.isingle.endowsingle can be used to calculate E[Z_{1}Z_{2}], z.ev.three.isingle.endowsingle can be used to calculate E[Z_{1}Z_{2}Z_{3}] and z.ev.twoone.isingle.endowsingle can be used to calculate E[Z_{1}^2Z_{2}] in Parker (1992).

Usage

## S3 method for class 'isingle.endowsingle'
z.moment(moment, ins, mort, irm)

z.ev.two.isingle.endowsingle(ins, mort, irm)

z.ev.three.isingle.endowsingle(ins, mort, irm)

z.ev.twoone.isingle.endowsingle(ins, mort, irm)

## S3 method for class 'isingle.endowsingle'
z.insrisk(ins, mort, irm)

## S3 method for class 'isingle.endowsingle'
z.invrisk(ins, mort, irm)

Details

The z.insrisk and z.invrisk functions for the endowsingle class are implemented such that we are conditioning on K not y. See Parker (1997) for details.

References

Parker, Gary. An application of stochastic interest rate models in life assurance. Diss. Heriot-Watt University, 1992.

Parker, G. (1997). Stochastic analysis of the interaction between investment and insurance risks. North American actuarial journal, 1(2), 55–71.

Examples

oumodel = iratemodel(list(delta0 = 0.1, delta = 0.06, 
alpha = 0.1, sigma = 0.01), "ou")
mort = mortassumptions(list(x = 40, table = "MaleMort91"))
endow = insurance(list(n = 10, d = 1, e = 1), "isingle", "endow")

z.ev(endow,mort,oumodel) # first moment
z.ev.two.isingle.endowsingle(endow, mort, oumodel)
z.ev.twoone.isingle.endowsingle(endow, mort, oumodel)
z.ev.three.isingle.endowsingle(endow, mort, oumodel)

nathanesau/stocins documentation built on May 23, 2019, 12:19 p.m.