On Annuities And The Social Pension Insurance With Stochastic Interest Rate

Mortality risk, expense risk and interest rate risk are three main risks for life insurance company. Mortality risk can be reduced by improving the technique of policy checking and expense risk can be decreased by enhancing the management, controlling the amount of production selling and cost reduction , but interest rate is difficult to be dispersed. An available approach to reduce the risk caused by the fluctuation of interest rate is to regard the interest rate as a random variable. At present, the domestic insurance companies just do little research in the stochastic rate, but staying at the studying of policy. With the globalization, liberalization and the general adoption of the market principle of finance, it seems to be necessarily to study the life insurance model with stochastic interest rate.The pricing of insurance products can not work without the assistance of insurance actuarial functions, The uncertainty of insurance actuarial functions is caused by two factors, the randomness of the remaining lifetime and the uncertainty of the future interest rate. The risk resulting from death can be reduced by selling large amount of contracts, which is guaranteed by the Law of Large Numbers, Whereas the risk engendered by fluctuating interest rate is difficult to be reduced, in this paper, traditional methods for life annuity are modified. The extension of the theory for life annuity to normal stochastic interest rate environment and its applications are discussed.Generally, the formulas of the distribution function and the moments of the present value of future payment streams for a policy or portfolio of policies are quite extensive, especially for the case of long-term discrete annuity, Therefore, the aim of this article is to discuss the present value or the accumulative value of several kinds of annuities with normal stochastic interest rate, deduce their accumulative distribution function as well as their mean and variance, the paper also analyzes the implicit pension debt in social pension system with stochastic interest rate and mortality environment and acquires the expected value and the variance of the present value of the pension benefits. The concrete expressions of the expected value and the variance are derived when the interest rate model is constructed with Wiener process.