几类风险模型中的破产概率研究

发布时间：2018-03-23 20:42

本文选题：破产时刻　切入点：破产概率　出处：《兰州交通大学》2012年硕士论文

【摘要】：本文研究了几类风险模型以及风险模型的改进模型的破产上界。主要运用了鞅方法和递归方法两种求解风险模型破产上界的方法对几类风险模型以及风险模型的改进模型进行预测和比较,从而得到哪种方法得到的结果拟合度更高,并且研究了公司破产中的相关变量对破产概率以及破产上界的影响。最终通过实例分析得到了降低公司破产风险的方法。本文共包括四章：第一章,概述了经典风险模型的背景知识以及在近百年间得到的一些有关精算方面的经典理论,已经取得的研究成果,介绍了两种得到最终破产上界的方法,同时简要介绍了本文的选题意义和内容。第二章,介绍了广义复合Poisson风险模型以及带扩展扰动项的复合Poisson模型,并给出了相应的破产概率的理论证明,并最终得到带干扰的非齐次Poisson风险模型破产概率上界,双复合Poisson风险模型破产概率上界,在实例分析中分别运用了两种求解方法求解破产上界并对结果进行比较。最后通过数值模拟比较出了它们的优劣性。第三章,总结和归纳了含有正、负风险和的模型和只含有负风险和的组合模型。从模型的构建着手,对两类模型进行对比并分别列出他们的数字特征。最终分别求解两类模型的破产概率的破产上界。第四章,从前几章对破产概率以及破产上界求解的基础上对两类Erlang(2)更新风险模型的破产概率以及破产上界进行分析和研究,首先介绍两类更新Erlang(2)风险模型,然后通过对传统风险模型的破产概率的研究方法对两类更新风险模型的破产概率进行求解,后又引出了Erlang(n)的一般性破产概率问题,并证明求解了Erlang(n)下和广义Erlang(n)下的罚金函数和破产概率。最终得到了Erlang(2)下的破产上界。文章最后进行了实例分析,并得出结论：防范利率风险,密切关注国家经济走势和银行政策是降低保险公司经营风险的有效保障；合理的公司并购是分散保险公司经营风险的有效途径。在几类方法求解保险公司破产上界的对比中递归方法明显优于鞅方法,鞅方法和递归方法较Lundberg上界又都有所改进和优化。
[Abstract]:In this paper, we study the ruin upper bounds of several kinds of risk models and their improved models. We mainly use martingale method and recursive method to solve the ruin upper bounds of risk models. Improved models for prediction and comparison, Finally, the method of reducing the risk of corporate bankruptcy is obtained by analyzing the influence of the relative variables on the ruin probability and the upper bound of bankruptcy. This paper consists of four chapters:. In the first chapter, the background knowledge of the classical risk model and some classical actuarial theories obtained in the past 100 years are summarized, and two methods to obtain the ultimate upper bound of bankruptcy are introduced. At the same time, it briefly introduces the significance and content of this paper. In chapter 2, the generalized compound Poisson risk model and the compound Poisson model with extended perturbed term are introduced, and the corresponding ruin probability theory proof is given. Finally, the upper bound of ruin probability of nonhomogeneous Poisson risk model with disturbance is obtained. The ruin probability upper bound of double compound Poisson risk model is solved by two methods in case analysis and the results are compared. Finally, the advantages and disadvantages of these two methods are compared by numerical simulation. In the third chapter, we summarize and summarize the model with positive and negative risk sum and the combination model with only negative risk sum. The two kinds of models are compared and their numerical characteristics are listed respectively. Finally, the ruin upper bound of the ruin probability of the two kinds of models is solved respectively. In chapter 4, we analyze and study the ruin probability and ruin upper bound of two kinds of Erlang2) renewal risk models based on the ruin probability and the solution of the upper bound of bankruptcy in the previous chapters. Firstly, we introduce two kinds of updated Erlang2) risk models. Then the ruin probability of two kinds of renewal risk models is solved by the method of studying the ruin probability of traditional risk model, and then the general ruin probability problem of Erlangn is introduced. It is proved that the penalty function and ruin probability under Erlangn) and generalized Erlangn) are solved. Finally, the upper bound of bankruptcy under Erlangn 2) is obtained. Paying close attention to the trend of national economy and bank policy is an effective guarantee to reduce the risk of insurance company management. Reasonable M & A is an effective way to disperse the business risk of insurance companies. The recursive method is obviously superior to the martingale method in the comparison of several methods to solve the upper bound of bankruptcy of the insurance company, and the martingale method and recursive method are both improved and optimized compared with the Lundberg upper bound.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F840

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