复合马尔可夫二项模型的红利策略

发布时间：2018-04-29 02:30

本文选题：复合马尔可夫二项模型 + Gerber-Shiu罚金函数　；参考：《湘潭大学》2013年硕士论文

【摘要】：在过去很长一段时间,关于保险公司红利策略的研究主要集中于连续时间模型,而离散时间模型中红利策略的研究也有其研究价值.在以往的离散时间模型研究中,主要以复合二项模型为主,但它的主要缺陷是假设保险公司索赔的发生是相互独立的,这与现实是相悖的.在我们生活的现实世界中,由于可能引发风险业务的共同因素存在,所以在本文中我们假设任意时刻索赔的发生与否都与它前一时刻的索赔情况有关,从而引入一个复合马尔可夫二项模型,它可以看成是复合二项模型的推广,在此模型中我们考虑几种红利的支付策略. 第一章绪论部分介绍与本文内容相关的研究背景和研究现状,以及本文选题的意义. 第二章主要讨论复合马尔可夫二项模型,并在该模型中引进一个常数红利边界策略,得到了Gerber-Shiu罚金函数所满足的线性方程组,且证得该方程组存在唯一解.最后,作为罚金函数的一些应用实例我们给出了一些具体风险量的计算公式. 在第三章中,我们在复合马尔可夫二项模型中考虑常红利边界策略下的红利期望现值,得到了红利期望现值所满足的方程组,且在相对宽松的条件下,求解出了直到破产发生时红利期望现值的近似解. 在第四章中,我们在复合马尔可夫二项模型中引进随机支付红利的策略,并在此策略下讨论Gerber-Shiu罚金函数.我们得到了罚金函数所满足的线性方程组、递推公式.作为罚金函数的特例,我们同样讨论了一些具体的风险量,并给出了相应结论.
[Abstract]:In the past a long time, the research on dividend strategy of insurance company is mainly focused on the continuous time model, and the dividend strategy in the discrete time model also has its research value. In the previous study of discrete time model, the compound binomial model is the main one, but its main defect is to assume that the claim of insurance company is independent of each other, which is contrary to the reality. In the real world where we live, because there are common factors that can trigger a risky business, in this paper we assume that the claim at any moment is related to the claim at the previous moment. Therefore, a compound Markov binomial model is introduced, which can be regarded as a generalization of the compound binomial model. In this model, we consider several dividend payment strategies. The first chapter introduces the research background and research status related to the content of this paper, as well as the significance of this topic. In the second chapter, we mainly discuss the compound Markov binomial model, and introduce a constant dividend boundary strategy in the model. We obtain the system of linear equations satisfied by the Gerber-Shiu penalty function, and prove the existence and unique solution of the system. Finally, as some application examples of the penalty function, we give some formulas for calculating the specific risk. In the third chapter, we consider the expected present value of dividend under the constant dividend boundary strategy in the compound Markov binomial model, and obtain the equations satisfying the expected present value of dividend, and under relatively loose conditions, An approximate solution to the expected present value of the dividend until the time of bankruptcy is obtained. In chapter 4, we introduce the strategy of random dividend payment in the compound Markov binomial model, and discuss the Gerber-Shiu penalty function under this strategy. We obtain the system of linear equations and the recurrence formula of the fine function. As a special case of penalty function, we also discuss some specific risk quantities and give corresponding conclusions.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;F224;O211.62

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