对偶风险模型中若干问题的研究

发布时间：2018-05-30 23:14

  本文选题：对偶风险模型 + 线性分红策略　； 参考：《湖南师范大学》2013年硕士论文

【摘要】：近些年来,在经典风险模型研究的基础上,同时有不少风险理论界的学者对它的对偶风险模型产生了兴趣.对偶风险模型的应用是相当普遍的,可以看成是保险公司、石油公司、科研发明公司等需要持续投资且收益不固定的企业.而对于风险模型的研究策略有很多,现在比较热门的是分红问题,常见的分红策略有两种：一种是常数门槛策略；另一种是阈红利边界策略.然而在实际生活中,分红边界常常是时刻变化并且依赖于时间,因而线性边界更具有实际意义.具有线性分红边界的风险模型最早是由Gerber在1974年提出来,他对经典的风险模型作了如下修正：盈余在边界水平以下时不发放红利；盈余在红利边界水平以上时便发放红利,直到发生下次索赔,如此运作的结果是盈余一旦越过红利界限便驻留在边界上.本文的前二章介绍了风险模型的背景及一些基本知识和结论,本文核心在第三章、第四章以及第五章. 本文第三章讨论了对偶风险模型的线性分红问题,给出了当oub时分红折现期望值V(u,b)满足的偏微分积分方程及一些边界条件；然后介绍矩母函数M(u,y,b)的定义和性质,推导出矩母函数所满足的偏微分积分方程及边界条件；最后得到n阶分红折现期望值Vn(u,b)所满足的偏微分积分方程. 第四章讨论了带干扰的对偶风险模型中的线性分红,给出了分红折现期望值V(u,b)、矩母函数M(u,y,b)和n阶分红折现期望值Vn(u,b)所满足的偏微分积分方程及边界条件. 第五章建立了随机观察下的对偶风险模型,给出了折罚函数mδ(u)所满足的方程,并且求得当密度函数为指数分布时折罚函数的显示解.
[Abstract]:In recent years, on the basis of the classical risk model, many scholars in the field of risk theory have been interested in its dual risk model. The application of dual risk model is very common. It can be regarded as insurance company, oil company, scientific research company and so on, which need to invest continuously and the income is not fixed. However, there are a lot of research strategies for risk model, but now the hot problem is dividend. There are two common dividend strategies: one is constant threshold strategy, the other is threshold dividend boundary strategy. However, in real life, the dividend boundary is always changing and dependent on time, so the linear boundary is more practical. The risk model with linear dividend boundary was first put forward by Gerber in 1974. He revised the classical risk model as follows: when the surplus is below the boundary level, it does not pay dividends, and when the surplus is above the dividend boundary level, it pays dividends. Until the next claim occurs, the result of this operation is that the surplus stays at the border once the dividend limit is crossed. The first two chapters of this paper introduce the background of the risk model and some basic knowledge and conclusions. The core of this paper is in the third chapter, the fourth chapter and the fifth chapter. In the third chapter, we discuss the problem of linear dividend for dual risk model, give the partial differential integral equation and some boundary conditions satisfying the expected value of dividend discounted when oub, and then introduce the definition and properties of the moment generating function Mu UU B). The partial differential integral equation satisfied by the moment generating function and the boundary conditions are derived. Finally, the partial differential integral equation satisfied by the expectation value of n order dividend discount is obtained. In chapter 4, we discuss the linear dividend in the dual risk model with disturbance, and give the partial differential integral equations and boundary conditions which are satisfied by the expectation value of dividend discounting, the moment generating function Mnuuyb) and the expectation value of n order dividend. In chapter 5, the dual risk model under random observation is established, the equation satisfied by the penalty function m 未 u) is given, and the explicit solution of the penalty function is obtained when the density function is exponential distribution.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：O211.63;F840.3

【参考文献】

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本文编号：1957245