Studies On Risk Model Of Insurance

In insurance mathematics,risk theory is the mainly contents of insurance risk theory,as can supply a very useful early-warning measure for the risk of the insurance company.It has important theoretical and practical significance for insurance company. Risk theory is mainly that how to make sure of the methods of probability and stochastic process to establish mathematical model, according to some actual situation about insurance company's management, and analysis its surplus process to give some means to calculate ruin probability. This paper has a lot of improvement from different angle in the foundation of classic risk model,so we obtain different risk model ,give some expressions for the ruin probability and discounted penalty function .In the classic risk model,premium is a constant,claim process is Possion process and its parameters is aconstant .Chaper 2 of this paper popularizes it from the following aspects:on one hand in the Markov environment premium varies with the state transtition, and the parameter of the Possion process also varies with the state transtition .On the other hand this paper consideres interest and investment factors,gives the connection of the two kinds of aspects.By analysis of the risk model,we discuss the ruin probability and show the effect of these factors, generalize the relate results.In chaper3 this paper considers Erlang(2) instead of Possion process and premium has connected with the surplus .This paper has only considers the surplus reaches precise number,premium will vary.This kind is two-step premiums.By analysis of the Gerber-Shiu discounted penalty function, we get integro-differential equation for Gerber-Shiu discounted penalty function, then use the especial result and common result of the integro-differential equation and some known result to obtain the expressions of Gerber-Shiu discounted penalty function.Finally all the works in this thesis are summarized and some prospects are proposed.