几类支付红利的离散时间风险模型的研究

发布时间：2018-10-25 20:13

【摘要】：随着保险业的发展和竞争的加剧,带分红的保险越来越多,带分红策略的风险模型的研究成为风险理论研究的热点课题.本文主要在几类离散时间风险模型基础上建立相应的带分红策略的风险模型,并研究了这些模型的Gerber-Shiu折现罚金函数、破产概率、破产持续时间、破产前盈余的分布、破产时破产赤字的分布等破产量的相关性质.主要的工作如下： 1.首先在复合马尔科夫二项模型的基础上,建立了一个支付红利的复合马尔科夫二项风险模型.给出了有条件和无条件的Gerber-Shiu折现罚金函数满足的瑕疵更新方程及其渐近估计,得到了有条件和无条件的破产概率、有条件和无条件的破产赤字的分布等破产量的递推公式及其渐近解. 2.讨论了红利界为一般非负整数的支付红利的双险种复合二项风险模型.对于盈余大于和小于红利界的情况同时进行了讨论,得到了两种情况下的Gerber-Shiu折现罚金函数满足的瑕疵更新方程及其渐进表达式和破产概率、破产赤字的分布等的递推公式. 3.研究了一个带特殊分红策略的离散时间风险模型.得到了该模型的Gerber-Shiu折现罚金函数所满足的差分方程以及边界条件,给出了其折罚函数的解析表达式,还给出了破产前盈余分布和破产持续时间分布的递推公式及其数值计算实例.最后将模型推广到更一般的更新风险模型.
[Abstract]:With the development of insurance industry and the aggravation of competition, there are more and more insurance with dividend. The research of risk model with dividend strategy has become a hot topic of risk theory research. In this paper, based on several discrete time risk models, the corresponding risk models with dividend strategy are established, and the Gerber-Shiu discounted penalty function, ruin probability, ruin duration and the distribution of surplus before bankruptcy are studied. The distribution of bankruptcy deficit at the time of bankruptcy and the related properties of output. The main work is as follows: 1. Based on the compound Markov binomial model, a compound Markov binomial risk model for dividend payment is established. In this paper, the defective renewal equation and its asymptotic estimate of conditional and unconditional Gerber-Shiu discounted penalty function are given, and the conditional and unconditional ruin probability is obtained. The recursive formula and its asymptotic solution for the distribution of conditional and unconditional ruin deficit. 2. In this paper, we discuss the compound binomial risk model of double insurance for dividend payment with a dividend bound as a general nonnegative integer. In this paper, we discuss simultaneously the case that the surplus is greater than or less than the dividend bound, and obtain the renewal equation of Gerber-Shiu discounted penalty function and its progressive expression, ruin probability, distribution of bankruptcy deficit, etc. 3. A discrete time risk model with a special dividend policy is studied. The difference equation and boundary conditions of the Gerber-Shiu discounted penalty function of the model are obtained, and the analytical expression of its commutation function is given. The recurrence formulas and numerical examples of surplus distribution and ruin duration distribution before bankruptcy are also given. Finally, the model is extended to a more general update risk model.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;F224;O211.67

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