几种再保险风险模型的研究

发布时间：2018-03-09 13:56

本文选题：风险模型　切入点：破产概率　出处：《燕山大学》2014年硕士论文　论文类型：学位论文

【摘要】：本文是在经典的复合Poisson风险模型的基础上，，对再保险风险模型进行研究，主要研究比例再保险和超额赔款再保险。根据实际需要，对复合Poisson过程进行推广，讨论保费收取次数为负二项随机过程，索赔次数为Poisson-Geometric过程的风险模型。首先介绍了相关的理论知识，对风险模型，破产概率，调节系数，鞅方法，负二项分布，Poisson-Geometric分布和Cox过程的相关理论进行了介绍。其次研究多险种的复合Poisson过程的再保险风险模型。首先研究复合Poisson过程的比例再保险风险模型，考虑了带有利率，通货膨胀率和破产下限的风险模型，得出了破产概率的表达式，当再保险比例系数越大时，调节系数越大，破产概率越小；然后研究复合Poisson过程的超额赔款再保险风险模型，得到了调节系数的上下界；最后考虑了带Cox过程的多险种风险模型，得出了破产概率的表达式，当原保险公司赔款上限越大时，调节系数越小，破产概率越大。接下来研究保费到达过程为负二项随机过程的再保险风险模型。首先研究负二项随机过程的比例再保险风险模型，得出了破产概率的表达式；其次考虑出现主索赔及延迟索赔时的风险模型，也得到了此模型的破产概率；最后研究负二项随机过程的超额赔款再保险风险模型，考虑了带有随机扰动项的风险模型，得出了当索赔为指数分布时，调节系数与超额赔款上限M的关系。最后研究复合Poisson-Geometric过程再保险的风险模型。首先研究复合Poisson-Geometric过程的比例再保险风险模型，考虑了退保事件，其中保费总额服从复合负二项随机过程，理赔总额服从复合Poisson-Geometric过程，退保总额服从复合二项随机过程，给出破产概率的表达式；其次研究复合Poisson-Geometric过程的超额赔款再保险风险模型，考虑了调节系数与超额赔款上限M的关系。
[Abstract]:In this paper, based on the classical composite Poisson risk model, the risk model of reinsurance is studied, the proportional reinsurance and excess reinsurance are studied. According to the actual needs, the composite Poisson process is generalized. This paper discusses a risk model in which the number of premium collection is negative binomial stochastic process and the number of claims is Poisson-Geometric process. Firstly, the relevant theories are introduced, such as risk model, ruin probability, adjustment coefficient, martingale method, negative binomial distribution Poisson-Geometric distribution and Cox process. Secondly, the reinsurance risk model of compound Poisson process with multiple types of insurance is studied. Firstly, the proportional reinsurance risk model of compound Poisson process is studied, and the risk model with interest rate, inflation rate and bankruptcy floor is considered. The expression of ruin probability is obtained, when the ratio coefficient of reinsurance is larger, the adjustment coefficient is larger, and the ruin probability is smaller. Then, the risk model of excess indemnity reinsurance in compound Poisson process is studied, and the upper and lower bounds of adjustment coefficient are obtained. Finally, the multi-insurance risk model with Cox process is considered, and the expression of ruin probability is obtained. When the upper limit of indemnity of the original insurance company is higher, the adjustment coefficient is smaller and the ruin probability is higher. Then we study the reinsurance risk model in which the premium arrival process is a negative binomial stochastic process. Firstly, the proportional reinsurance risk model of the negative binomial stochastic process is studied, and the expression of ruin probability is obtained. Secondly, considering the risk model of the main claim and the delay claim, the ruin probability of the model is also obtained. Finally, the risk model of excess indemnity reinsurance for the negative binomial stochastic process is studied, and the risk model with random disturbance is considered. When the claim is exponentially distributed, the relationship between the adjustment coefficient and the upper limit M of excess compensation is obtained. Finally, the risk model of reinsurance in compound Poisson-Geometric process is studied. Firstly, the proportional reinsurance risk model of compound Poisson-Geometric process is studied, and the event of reinsurance is considered, in which the total premium is from the compound negative binomial stochastic process, and the total claim is from the compound Poisson-Geometric process. The expression of ruin probability is given from the compound binomial stochastic process. Secondly, the risk model of excess indemnity reinsurance in compound Poisson-Geometric process is studied, and the relationship between the adjustment coefficient and the upper limit M of excess indemnity is considered.
【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F840.3;F224

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