关于一类随机收入风险模型的研究

发布时间：2018-04-03 16:43

本文选题：随机收入　切入点：地偶风险模型　出处：《湖南师范大学》2013年硕士论文

【摘要】：风险理论是精算数学的核心内容,因此这也引起越来越多从事经济与保险行业的研究人员的关注.众所周之,经典的风险模型及其推广模型主要考虑保费收入是连续的.然而,保费连续性在风险模型的应用中有很大的局限性.为了使模型更加符合保险公司的实际运作,很多学者将随机收入风险模型引入到风险理论中.近些年来,保费的随机化成为风险模型研究的热点课题.本文主要考虑了一类具有随机收入风险模型的破产相关问题,并得到了一些相关结论.本文的主要结构如下：第一章,首先,简单的分析了风险问题的研究背景及其最新研究动态.其次,介绍了本文研究的一些破产相关特征量最后,阐述了本文主要的研究内容及其结论. 第二章,主要介绍了本文所涉及的一些基本知识点,同时还简单的引入了几类随机收入风险模型. 第三章,考虑了阈值分红策略下广义的Erlang(n)对偶风险模型.在经典的风险模型中,保费的收取是连续的,而索赔过程为复合Poisson过程.然而在一些公司(药物的研发以及石油的开采)实际运作中,用连续的开销以及随机的收益来描述公司的运作则更加符合实际问题.本章得到了期望折现分红总量以及破产概率满足的积分-微分方程及其边界条件.当跳跃的等待时间及其大小分别服从不同参数的指数分布时,我们得到了期望折现分红总量与破产概率的显示解析式.同时,在给定一些参数的具体数值情况下,求出了期望折现分红总量与破产概率的数值表达式. 第四章,主要考虑了由布朗运动扰动的随机收入风险模型,假定随机保费收益过程以及随机索赔过程分别为Poisson过程与广义的Erla-ng(n)过程且单个保费收益的大小是服从参数为β-1的指数分布.通过计算推导出Gerber-Shiu折罚函数的拉普拉斯变换的显示表达式,最后运用拉格朗日差值公式得到了折罚函数的渐近表达式及其数值解.
[Abstract]:Risk theory is the core of actuarial mathematics, so more and more researchers engaged in economics and insurance industry pay attention to it.As we all know, the classical risk model and its extension model mainly consider that premium income is continuous.However, premium continuity has great limitations in the application of risk model.In order to make the model more in line with the actual operation of insurance companies, many scholars introduce the stochastic income risk model into the risk theory.In recent years, the randomization of premium is a hot topic in risk model research.In this paper, we consider the ruin problems of a class of stochastic income risk models and obtain some relevant conclusions.The main structure of this paper is as follows:In the first chapter, the research background and the latest research trends of the risk problem are briefly analyzed.Secondly, the paper introduces some characteristic quantities of bankruptcy. Finally, the main contents and conclusions of this paper are described.The second chapter mainly introduces some basic knowledge of this paper, and introduces several kinds of stochastic income risk models.In chapter 3, we consider the generalized Erlangn) dual risk model under threshold dividend strategy.In the classical risk model, the premium collection is continuous, while the claim process is a compound Poisson process.However, in the actual operation of some companies (drug research and development and oil extraction), it is more realistic to describe the company's operation with continuous expenses and random income.In this chapter, we obtain the integro-differential equations and boundary conditions of the total expected discounted dividends and the ruin probability.When the waiting time and the size of the hopping are obtained from the exponential distribution of different parameters, we obtain the expression of the total expected discounted dividend and the ruin probability.At the same time, the numerical expressions of the total amount of expected discounted dividends and the ruin probability are obtained under the condition of given the specific values of some parameters.In chapter 4, the stochastic income risk model, which is disturbed by Brownian motion, is considered.The stochastic premium return process and the stochastic claim process are assumed to be Poisson processes and generalized Erla-ngn processes, respectively, and the size of a single premium income is an exponential distribution with a parameter of 尾 -1.The display expression of Laplace transform of Gerber-Shiu penalty function is deduced by calculation. Finally, the asymptotic expression of penalty function and its numerical solution are obtained by using Lagrange difference formula.
【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】：O211.6;F840.3

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