复合多险种风险模型破产概率估计

发布时间：2018-09-18 16:04

【摘要】：本文研究了保险公司多险种经营的破产问题.通过对调节系数存在性,破产概率上界与生存概率微分方程的研究,给出了复合多险种风险模型下破产概率的估计方法,从而使风险模型可以更科学地为保险实务服务.具体的研究内容及成果如下:首先,研究了复合多险种险种风险模型的破产概率问题.利用平稳独立增量过程的性质,证明了调节系数的存在性,得到了该模型下的破产概率上界.同时应用MATLAB软件研究了特值条件下多险种对该模型破产概率上界的影响.本文还研究了此模型的生存概率问题.利用范德蒙矩阵的性质,得到了该模型在收入和索赔过程服从Poisson过程时生存概率的微积分方程,并给出了收入额和索赔额服从指数分布下该方程的通解.
[Abstract]:This paper studies the bankruptcy of insurance companies with multiple types of insurance. Through the study of the existence of adjustment coefficient, the upper bound of ruin probability and the differential equation of survival probability, a method of estimating the ruin probability under the compound multi-type risk model is presented, which makes the risk model serve insurance practice more scientifically. The specific research contents and results are as follows: firstly, the ruin probability of the multiple insurance risk model is studied. By using the properties of stationary independent incremental processes, the existence of the adjustment coefficient is proved, and the upper bound of ruin probability is obtained under the model. At the same time, the influence of multiple types of insurance on the upper bound of ruin probability of the model is studied by using MATLAB software. This paper also studies the survival probability of this model. By using the properties of Van der Mon matrix, we obtain the calculus equation of the survival probability of the model for the income and claim process from the Poisson process, and give the general solution of the equation under the exponential distribution of the income and claim amount.
【学位授予单位】：延安大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F840.4

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