Insurance Policies And Claims Of Time-dependent Risk Model Bankruptcy

Ruin theory for long-term and stable business of the insurance company has the extremely vital significance, so which is the concern of insurance company. Ruin the-ory is the core of risk. The Lundberg-Cramer classical risk model is the first risk model that the theory of ruin posed. Depending on the Lundberg-Cramer classical risk model, we always assume the premium income to a linear function, policy and claim to reach several independent of each other. In fact, it is not enough to describe the reality. So many cases of dependency risk model are studied by more and more scholars. Basing on the Lundberg-Cramer classical risk model, I promote it to more general situation in this paper. Thus we get a dependent risk model, if it satisfied:the premium income is not constant, but a random variables, the arrival of the term policies{M(t)} follows a Poisson process, the arrival of the term policies{M(t)} and the occurrence of the claim {N(t)} is dependent, the{N(t)} is the p-thinning process of the{M(t)}. In this paper, we get the joint density function of the three characteristics of the ruin probability of the dependent risk model. Using the method of martingale and stopping time, we also get the general expression of the eventual ruin probability and an upper bound estimation of the ruin probability. Finally we get the concrete exprssion of ruin probability when the premium and claim charge follow the exponential distribution. We also compare the upper bound of the Lundberg-Cramer classical risk model with the upper bound of the dependent risk model. The upper bound of the dependent risk model is smaller than the Lundberg-Cramer classical risk model, so it is significant to study the dependent risk model.According to the contents, this paper be divided into three chapter:In the first chapter, I introduces the research status of risk model and some main achievements of scholars. Then I simply introducts the thinning process which is prepared for the following content.In the second chapter, firstly, I introduce the Lundberg-Cramer classical risk model simply. Then I get the dependent risk model by the thought and principle of the Lundberg-Cramer classical risk model. In the third chapter, I introduce the prepare knowledge and main results, including the joint density function of the three characteristics: and the ruin probability Lundberg upper and ultimate ruin probability is studied through numerical calculation, the initial reserve, the changes and the policy and manage the relationship between the management of insurance company. Through the new data cal-culation model and the upper bound of the Lundberg-Cramer classical risk model were compared.