Study On Risk Model With Random Premium Under Heavy-tailed Claims

In actual operation of insurance companies, on the one hand, as a result of the influence of competition, interest rate and other environmental factors, premium and the time of charged premium both are random variables; On the other hand, emergent events have an enormous crisis on the business of insurance company, such as earthquakes, fires, floods and so on. Great losses that are caused by extreme events need to be drawn by heavy-tailed theory. Moreover, the study on finite time ruin probability tends to be more practically significant. So the risk model of random premium under heavy-tailed claims is put forward creatively in the thesis. And it can be used to generalize the model in the existed documents in a way that accords with reality. At the same time, the asymptotic equivalent form of ruin probability in (0,t] t is taken into consideration. The main research results of the full text are as follows:Firstly, the risk model of random premium with the loss distribution belongs to the family ofL^*_m is established. It is assumed that the claim process is Poisson process and premium-arrival process is an ordinary renewal process. By using probability theory and methods of random processes, an important asymptotic equivalent form in (0,t] t is obtained. Then the risk model is extended to the generalized delayed renewal risk model. The claim sizes and the claim intervals have different distributions respectively in this model. What’s more, an important asymptotic equivalent form in (0,t] t under the class L^*_m is obtained.Secondly, the risk model of random premium and random delays under heavy-tailed claims is taken into account. It is assumed that the claim sizes and the claim intervals have different distributions respectively in this model, and the number of delay is random. Then an important asymptotic equivalent form in (0,t] t under the classL^*_m can be studied and discussed.Finally, the risk model of heavy-tailed claims, interest rate, random premium and two kinds of claims that are taken into account is established. The existing models are extended. It is assumed that the claim process is Poisson process and premium-arrival process is an ordinary renewal process in the model. By virtue of probability theory and methods of random processes, an important asymptotic equivalent form in (0,t] t is obtained.