The Application Of Martingale Method In Risk Model

The study of the ruin probability is an extremely important question in risk theory, that is the probability of insurance company's earning being negative at the fist time. The ruin probability can provide an alarm for decision maker of insurance companies, also is a measure of finance risk, thereby, the study of it has important guiding significance to management of insurance companies and supervising of insurance surveillance departments. Martingale is a theory in the front of stochastic process. Recently, it was gradually applied to various disciplines. Using Martingale theory to study risk models not only has important theoretic significance but also the practical value.This paper introduced the knowledge about martingale and the classical risk model, used the diffusion approximation to compute the finite time ruin probability of this risk model, and used Martingale theory to estimate the upper bound of the ruin probability. But in the classical risk model, the premium process is a time linear function, has not considered the influence of stochastic factors. The classical risk model has limitation with the expansion of business.Based on literatures, we extended the classical risk model, defined the model in which premium income was a generalized compound Poisson process. The author validated additivity of this process, and simplified the model. The theories of martingale and diffusion approximations are applied to this model. We got some useful results about the ruin probability and the finite time ruin probability.This paper constructed the multi-insurance risk model from the special to the general with scientific method. The author specially dealt with the two-insurance risk model, calculated the ruin probability, then extended it to the multi-insurance risk model.