三类复合风险模型破产问题的研究

发布时间：2018-04-08 14:44

  本文选题：Poisson过程　切入点：复合Poisson-Geometric过程　出处：《南华大学》2014年硕士论文

【摘要】：风险理论是概率论与数理统计研究中的一个重要分支，也是精算数学研究的核心内容，而破产理论又是风险理论的核心内容。近年来，很多学者对经典的风险模型进行了推广，，并取得一定成果。本文在已有成果基础上做了进一步研究，主要包括以下几个方面： 第一、将经典风险模型推广为保费收取为Poisson过程,赔偿次数为二项过程的离散风险模型,用微分方法证明了调节系数的存在性，用矩母函数法推导出其破产概率表达式，且该表达式与经典风险模型结论一致。 第二、推广了保费到达过程,考虑到风险事件与赔付事件不一定等价的实际情况，将理赔过程推广为复合Poison-Geometric过程，并引入了随机干扰项，建立了带有干扰条件下多险种风险模型，推广了相关文献的结论。 第三、将经典风险模型推广为保费收取为Poison过程,索赔次数为复合Poison-Geometric过程的带干扰风险模型，不仅研究了模型的破产概率，同时也得到了生存概率的一个积分微分方程，这些结论对保险公司评估风险具有一定指导意义。
[Abstract]:Risk theory is an important branch of probability theory and mathematical statistics, and it is also the core content of actuarial mathematics research, and bankruptcy theory is the core content of risk theory.In recent years, many scholars have generalized the classical risk model and achieved some results.Based on the existing results, this paper makes further research, mainly including the following aspects:Firstly, the classical risk model is generalized to a discrete risk model in which the premium is collected as a Poisson process and the compensation is a binomial process. The existence of the adjustment coefficient is proved by differential method, and the ruin probability expression is derived by the moment generating function method.The expression is consistent with the conclusion of the classical risk model.Secondly, the premium arrival process is generalized, and considering the fact that the risk event and the indemnity event are not necessarily equivalent, the claim process is generalized to the compound Poison-Geometric process, and the stochastic disturbance term is introduced.The risk model of multiple types of insurance with interference is established, and the conclusion of relevant literature is extended.Thirdly, the classical risk model is extended to the Poison process with premium collection and the number of claims is the complex Poison-Geometric process. The ruin probability of the model is studied, and an integro-differential equation of survival probability is obtained.These conclusions have certain guiding significance for insurance companies to assess risk.
【学位授予单位】：南华大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：O211.6;F840.3

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