关于分红策略下的离散风险模型的研究

发布时间：2018-04-25 14:57

本文选题：复合二项风险模型 + 随机收入　；参考：《湖南师范大学》2013年硕士论文

【摘要】：破产理论是近几年来风险理论研究的一个热点课题.本文在经典复合二项模型的基础上,通过在保费收入,索赔额分布等方面进行推广从而得到了不同离散的风险模型,并重点研究了Gerber-Shui折罚函数,期望折现分红总量等破产特征量,主要做了下面几个方面的工作： 1.基于具有随机分红的复合二项风险模型,将保费进行推广,不再是关于时间的一个线性函数,而是一个二项过程.在该模型下,我们得到了折罚函数的递推公式以及通过一个线性方程组来确定的Φ(0)(初始值为零时的Gerber-Shui折罚函数的值).最后,证明了线性方程组的解的唯一性以及给出了更新方程的解. 2.在随机回报的复合二项风险模型的基础上,将该模型推广为带随机回报的一类离散马氏风险模型,赔付的发生概率,赔付额的分布函数都有一个离散的马氏链调控,当保险公司采用门槛分红策略时,通过计算得到了破产前的期望折现分红总量满足的一组线性方程组.最后,给出了期望折现分红总量的显示解析式. 3.在具有常红利边界和延迟索赔的一类更新离散的模型上,将保费收入进行推广为一个二项过程,通过计算我们得到了带新的边界条件的期望折现分红总量的微分方程组.最后,给出了期望分红总量的显示解析式.
[Abstract]:Bankruptcy theory is a hot topic in risk theory research in recent years. On the basis of the classical compound binomial model, the different discrete risk models are obtained by extending the premium income and the distribution of claim amount, and the Gerber-Shui penalty function is studied emphatically. Expected discounted dividends and other bankruptcy characteristics, mainly do the following aspects of work: 1. Based on the compound binomial risk model with stochastic dividend, the premium is generalized, which is no longer a linear function of time, but a binomial process. In this model, we obtain the recursive formula of the folding penalty function and the value of the Gerber-Shui penalty function determined by a linear equation set (the initial value is 00:00). Finally, the uniqueness of the solution of the linear system is proved and the solution of the renewal equation is given. 2. On the basis of the compound binomial risk model of random return, the model is extended to a discrete Markov risk model with random return. The probability of compensation and the distribution function of indemnity have a discrete Markov chain control. When the insurance company adopts the threshold dividend strategy, a set of linear equations for the total expected discounted dividend before bankruptcy is obtained by calculation. Finally, the display analytic formula of the total amount of expected discounted dividends is given. 3. On a class of updated discrete models with constant dividend boundary and delay claim, the premium income is generalized to a binomial process. By calculating the differential equations with new boundary conditions, we obtain the total expected discounted dividends. Finally, the display analytic formula of the total amount of expected dividends is given.
【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】：F842.3;O211.63

【参考文献】