一类相依结构的稀疏风险模型的周期分红研究

发布时间：2018-03-20 18:07

  本文选题：稀疏过程　切入点：保费随机化　出处：《曲阜师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：经典风险模型中以常数比率收取保费,但在保险公司的现实经营中,保费的收入是随机的,且通常是与索赔的发生相关的.因此,本文中考虑了一类相依结构的稀疏风险模型,在该模型中,假设保单的到达过程是参数为λ的Poisson过程,同时索赔到达过程是该Poisson过程的一个P-稀疏过程.Gerber与Shiu(1998)首先提出了Gerber-Shiu函数(也称为期望折现罚金函数),提供了一个可以同时解决多个精算量的统一方法.De Finetti(1957)初次提出了分红问题,目前分红问题是研究热点.本文考虑了一类稀疏风险模型,研究了在常数barrier策略和周期分红策略下的期望折现罚金函数和期望折现累计分红函数,得到了它们分别所满足的积分方程,同时也获得了在特殊情况下的具体表达式以及破产概率的精确表达式.第一章为绪论,介绍了一类相依结构的稀疏风险模型,以及周期分红研究的背景及现状.第二章为预备知识和模型介绍,重点介绍了稀疏风险模型和周期分红策略,以及Gerber-Shiu函数等基本概念.第三章和第四章是本文中的主要研究成果,第三章得到了带有周期分红策略的稀疏风险模型的期望折现罚金函数所满足的积分方程当,当u b时.同时得到了在索赔额和保费额同时服从指数分布时的期望折现罚金函数的具体表示式最后获得了破产概率的精确表达式第四章主要研究了带有周期分红策略的稀疏风险模型的期望折现累计分红函数所满足的积分方程当0 ≤ u ≤ 6 时,当u 6时,.以及在索赔额和保费额同时服从指数分布时的期望折现累计分红函数的精确表达式.第五章对本文进行了总结.
[Abstract]:In the classical risk model, the premium is charged at a constant rate, but in the real operation of an insurance company, the premium income is random and usually related to the occurrence of claims. Therefore, a class of sparse risk models with dependent structures are considered in this paper. In this model, it is assumed that the policy arrival process is a Poisson process with a parameter 位. The simultaneous claim arrival process is a P- sparse process of the Poisson process. Gerber and Shiu (1998) first proposed the Gerber-Shiu function (also known as the expected discounted penalty function, which provides a unified method to solve multiple actuarial quantities simultaneously. De Finettitio 1957). The issue of dividends is raised. In this paper, we consider a kind of sparse risk model, and study the expected discounted penalty function and the expected discounted cumulative dividend function under the constant barrier strategy and the periodic dividend policy. The integral equations which they satisfy are obtained respectively. At the same time, the concrete expressions and the exact expressions of ruin probability in special cases are obtained. The first chapter is an introduction, which introduces a class of sparse risk models with dependent structures. The second chapter is the introduction of preparatory knowledge and model, focusing on sparse risk model and periodic dividend strategy. Chapter 3 and chapter 4th are the main research results in this paper. In chapter 3, the integral equation of the expected discounted penalty function of the sparse risk model with periodic dividend strategy is obtained. When u b, the exact expression of the expected discounted penalty function for both the claim amount and the premium amount is obtained. Finally, the exact expression of ruin probability is obtained in Chapter 4th. The integral equation satisfied by the expected discounted cumulative dividend function of sparse risk model of red strategy is 0 鈮，

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