The Study About Actuarial Model Of Life Insurance With Stochastic Interest Rate

The human being must face to all kinds of risk in society. The risk shows it with uncertainty, suddenness and unexpectedness locally, while stabilization and consistency wholly. Life insurance is a kind of long-term economic-behavior, and huge difference between expectation and the fact would be brought. According to traditional actuarial theory, interest rate is certain, and that is for simplification of researches. After meticulous calculation and analysis, insurance companies design insurance variety rationally, and compensate insurance-policy holders normally in the one hand and do some investment reasonably in the other hand. It is the best choice for insurance companies to choose stochastic interest rate models, design insurance-variety in order to attract client and enhance income.The stochastic interest rate models are attended by researchers. After summarizing the results which have existed, this article step farther into the researchesSection 1, contains the history of insurance, the situation of insurance actuarial theory today and the tide of development in the future. The emphases are to explain the disadvantages of fixed interest rate actuarial models and the advantage of stochastic interest rate actuarial models. This paper also gives the need for stochastic interest rate models.Section 2, included is content of interest rate theory. As the base for researches about stochastic interest rate models, this section emphasizes accumulated function, compound interest and the force of interest.Section 3 talks about survival function, time-until-death and life table, and gives the rule of life distribution.Section 4 introduces the characters of life insurance; the calculation about annuity with fixed interest rate, based on that, the calculations of annuity, under stochastic interest rate, with discrete time, formula about expectation and variance of current value and formula about reasoning relation between them are given; enumerates the basic models of life insurance and annuity; the theory of balance and two methods on current value, named past method and future method, and the formula of the expectation and variance of current value of premium reserve under stochastic interest rate; a kind of continuous life insurance actuarial model of 2 dimensions life state, the function of force of interest rate is built with Brownian Motion and reflected Brownian Motion, the formula of net level premium and the concise formula of net level premium under even distribution are given.