The Study On Some Risk Models With Dependent Relationship And Reinsurance Strategy

This article has outlined the research and development of the risk theory, and summarized the classic risk model in detail in the domestic and overseas present research situation as well as the constituent and the main results of the classic continuous risk model. Based on this, in view of the gradually complex and specific situation on present actual insurance business, by taking the surplus capital being invested, the dependent relationships and affection of reinsurance in risk model, in this article I have studied the bankrupt parameter of this model, so that the actual operation situation of insurance company can be reflected more truly and accurately, and it's helpful for the insurance company to make the overall plan arrangement in insurance business.This article firstly introduced a dependent risk model with investment and interference. After analyzing the proposed model, the stationary-increment properties of the profit process and the statistical character of the risk process were obtained. And the formula of the ultimate ruin probability and its Lundberg inequality were also derived.Secondly, considering a dependent risk model with reinsurance and interference, it is more sensible to study the digital characteristics of earning process in the model, final ruin probability, Lundberg inequality and so on. Finally, various trend of the optimal strategy is simulated analytically along with changing many parameters. In fact, in the process of the insurance company's operation, there are some random factors once for a while, which makes client choose to reinsurance business, and considering the reinsurance is heuristic to operate the insurance business.Thirdly, the application of reinsurance on compound Poisson-Geometric risk model is discussed. With the development of the insurance business, there is a new scheme of paying deductible amount. Because the payment scheme leads to some errors between the practical number of claims and the number of claims, the Poisson-Geometric process which can describe the errors by using its parameter is introduced so that insurer can do better for operating the insurance business. With premiums' policy influencing the number of claims, a new and practical multitype-insurance risk model which is described by Poisson process and Poisson-Geometric process is set up, and the results are heuristic to operate the insurance business. Under the above each kind of model, namely the earnings process is a steady independent increment process, which obtained the concrete expression form of ruin probability, especially more importantly had found the upper boundary of ruin probability, that is the Lundberg inequality, it is widely applied in the insurance system's risk analysis for its strong feasibility, which has the important theoritical and the practical significance.Lastly, a risk model with investment under fuzzy rate of interest is studied. Because random interest which is involved in insurance business is fuzzy random variables, a risk model under fuzzy rate of interest is heuristic to operate the insurance business. Then We discussed the baisc property, ruin probability and its upper bound of the model mathematically. The results of the ruin probability characteristics provide some good ideas for insurance company to prevent some risks.