The Establishe And Analysis Of Actuarial Model Of Life Insurance Under The Stochastic Interest

Actuarial science applies the knowledge and principles of mathematics, statistics, finance, insurance and demography in the quantitative analysis of all aspects with the management of the insurance industry, providing scientific basis and tools for raising the level of management and making strategies. With the development of insurance, actuarial science is more and more important.Life insurance is a long-term business, interest rate is an important factor in calculating of premium and reserves. The traditional actuarial theory mainly uses deterministic interest rate. However, because guarantee contract is a long-term economic behavior, many factors such as government policy and economy cycle will bring about the uncertainty of interest rate, the study on insurance premium, reserve under stochastic interest rate gradually becomes one of hotspots in actuary theory.This article focused on presenting stochastic process for modeling the force of interest, First, continuous life insurance model and semi-continuous life insurance model were established respectively by Wiener Process for modeling the force of interest. Then considering abrupt event's effect on interest, continuous life insurance model and semi-continuous life insurance model were established respectively by Brown Process and Poisson Process jointly for modeling the force of interest. Then, according to the basic principle of life insurance, derived survival annuity, the balanced pure insurance premium and the loss variable under these two kinds of stochastic interest models. We use numerical simulation to analyze the necessity of the stochastic interest rate. Late we compare the calculating of premium and reserves and loss variable under constant rates, Wiener Process model, Wiener Process and Poisson Process jointly model, which reflect the practicability of stochastic interest rate and also provide theoretical support to the operation of insurance companies.