Study On Continuous Increasing Payment Life Insurance With Random Interest Rate

The risk of the interest rete is always the most important factor to insurance company.Even if there is a tiny alteration,it would be a tremendous fluctuation on the operation;therefore it would influence the daily managent.Interest randomness in life insurance has paid attention to in recent years on actuarial theory and its application.In this paper,n-year increasing payment life insurance with the stochastic interest with continuous conditions was discussed.Common increases the volume life insurance form to have linear,the geometry grows and the exponential growth.The common death rate supposition has four kinds: De Moivre death rate,Gompertz death rate,Makeham death rate and Weibull death rate.First,models of the random rate of interest were established respectively by Wiener process or Brown process.The moment and variance of the payable present vale under the two eases were griven.Moreover,the special expression of the moment and the variance with four different death rate were given.Then considering abrupt event's effect on interest,we established the models of the random rate of interest jointly by Brown process and Poission pression,or Brown process and Negetive Binomial Bistribution,also gave the moment and the variance of the payable present value under the two cases.Moreover giving the special expression of the moment and variance with four different death rates.