The Risk And Stochastic Problems In Life Insurance

Actuarial theory is very important in the modern insurance industry. Usually, the traditional theory is based on a fixed interest rate. However the fact of government policy and economic cycles may cause the interest rate to be uncertain during the time of insurance, the study on actuarial theory and method under stochastic rates of interest has become an important and popular topic from 1970s. This article dose the detailed analysis to the premium and its stability about increasing life insurance under different stochastic interest models firstly, and then dicusses the application of Markov chains in serious sickness insurance.This thesis is organized as follows:Chapter 1 is introduction. It gives introductions to the development and research of life insurance actuarial theory under stochastic interest rate. It also introduces the main work of this article.Chapter 2 discusses the preliminary knowledge of actuarial theory. A series of stochastic interest models are also gived in this part.Chapter 3 and chapter 4 is the main part of the paper. In chapter 3, the premiums about increasing life insurance under different stochastic interest models are studied by introducing the reserve process, a numerical example is given to calculate and analyze. At the same time, the prensent value of a special increasing life insurance is canvassed. In chapter 4, the application of Markov chains in serious sickness insurance is discussed and reserves are computed.