混合分红策略下的复合泊松风险模型

发布时间：2018-06-05 17:14

本文选题：复合泊松模型 + 混合分红策略　；参考：《重庆大学》2016年硕士论文

【摘要】：在这篇文章中,我们考虑了混合分红策略下的复合泊松风险模型。混合分红策略是门限障碍分红策略和周期性分红策略的复合。给定一个正的门限水平b,只要盈余过程中盈余水平超过b,就以速率a0进行连续地分红。进一步,给定一个分红决定时间序列,当在分红决定时间jZ处观测到的盈余水平超过b,就将超出部分作为红利分出去。在经典复合泊松风险模型中将两种分红策略结合引入,不仅解决了引入单一分红策略的缺陷,同时也更具有实际意义。在文章中,我们对混合分红策略下风险模型的破产前的期望折现分红函数和Gerber-Shiu期望折现罚金函数进行了研究,并就以研究结果给出一些数值例子。本文的结构和内容安排如下:第一章,介绍了风险模型研究背景和意义,经典复合泊松风险模型以及带分红策略的风险模型的研究现状。第二章,该部分介绍了文章中将要用到的概念,公式以及一些相关性质,主要涉及到拉普拉斯变换及部分分式展开法求拉普拉斯逆变换,Dickson-Hipp算子等。第三章,这部分我们主要对引入了门限分红和周期性分红策略后的混合分红策略风险模型进行了详细的介绍。第四章,这是文章的核心部分。在具有混合分红策略的风险模型的中,考虑模型的Gerber-Shiu罚金函数和期望折现函数的满足的方程,并求出显式解。第五章,为了更好地解释我们在第三章得到的结果,我们给定参数值,在三种不同的索赔额密度函数下,通过图像的形式,直观地呈现了Gerber-Shiu期望折现罚金函数和期望折现分红函数的一些性质。
[Abstract]:In this paper, we consider the compound Poisson risk model under the mixed dividend strategy. The mixed dividend strategy is a combination of threshold barrier bonus strategy and periodic dividend strategy. Given a positive threshold level b, as long as the surplus level in the surplus process exceeds b, the dividend is continuously distributed at the rate of a 0. Further, given a dividend decision time series, when the surplus level observed at the dividend decision time jZ exceeds b, the excess part is divided as a dividend. The combination of two dividend strategies in the classical compound Poisson risk model not only solves the defect of introducing a single dividend strategy, but also has practical significance. In this paper, we study the expected discounted dividend function and the Gerber-Shiu expected discounted penalty function of the risk model under the mixed dividend strategy, and give some numerical examples. The structure and content of this paper are as follows: in Chapter 1, the background and significance of the research on risk model, the research status of classical compound Poisson risk model and risk model with dividend policy are introduced. In the second chapter, this part introduces the concepts, formulas and some related properties of the paper, mainly involving Laplace transform and partial fractional expansion method to solve the inverse Laplace transform Dickson-Hipp operator and so on. In chapter 3, we introduce the risk model of mixed dividend strategy after introducing threshold dividend and periodic dividend. The fourth chapter, this is the core part of the article. In the risk model with mixed dividend strategy, the equations of the Gerber-Shiu penalty function and the expected discount function of the model are considered, and the explicit solution is obtained. In chapter 5, in order to better explain the results we get in Chapter 3, we give the parameter values, in the form of images, under three different claims density functions. Some properties of Gerber-Shiu 's expected discounted penalty function and expected discounted dividend function are presented intuitively.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F224

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