随机分红策略下离散风险模型的研究

发布时间：2018-10-20 16:24

【摘要】：当公司运用确定性分红策略时,需要时刻关注盈余水平变化来决定是否进行分红,且当盈余水平具有很多的波动点时,公司可能在很短的时间内做出多次分红,这样必然会增加公司的运营成本。为了解决上述确定性分红策略中的缺陷问题,风险理论研究领域提出了随机分红策略。而公司在经营过程中,诸如收入、索赔、分红等过程通常都是离散的,研究离散风险模型具有现实意义。本文主要研究两类具有随机分红策略的离散风险模型,对风险模型中的分红情况、Gerber-Shiu函数以及破产概率进行研究,本文的结构和内容安排如下。第一章,首先介绍经典风险模型以及其重要定义与概念,其次对其国内外研究现状进行简单的回顾,再次介绍本文模型推广的基础—复合二项风险模型,最后给出本文的主要研究内容。第二章,主要介绍本文将要频繁用到的几个重要概念:生成函数、卷积和Dickson-Hipp算子的定义和相关性质,同时给出本文常用的一些符号的定义。第三章,考虑一个加入随机分红策略的马尔科夫调节风险模型,首先介绍模型的基本情况,然后运用生成函数及其反变换等方法,通过严谨的数学推导,得到Gerber-Shiu函数的递推公式,从而得到破产概率的递推公式并给出了一个特殊情形下的数值算例。第四章,考虑一个加入随机分红策略的延迟赔付风险模型,主要通过生成函数及其反变换的方法,借助构造的辅助模型,结合数学与概率论的方法,推导出期望分红现值的表达式,随后在理赔额为常数的情况下得到一个数值算例。
[Abstract]:When a company applies a deterministic dividend strategy, it needs to pay close attention to the change of earnings level to decide whether to pay dividends or not, and when the earnings level has a lot of fluctuations, the company may make several dividends in a very short period of time. This will inevitably increase the company's operating costs. In order to solve the defect problem in the deterministic dividend strategy mentioned above, a stochastic dividend strategy is proposed in the field of risk theory. However, in the process of business, such as income, claim, dividend and so on, the process is usually discrete, the study of discrete risk model has practical significance. In this paper, two kinds of discrete risk models with stochastic dividend strategy are studied. The dividend, Gerber-Shiu function and ruin probability in the risk model are studied. The structure and content of this paper are arranged as follows. In the first chapter, we introduce the classical risk model, its important definition and concept, then review the current research situation at home and abroad, and then introduce the basic binomial risk model which is popularized in this paper. Finally, the main research contents of this paper are given. In the second chapter, we mainly introduce some important concepts that will be used frequently in this paper: the definition and properties of generating function, convolution and Dickson-Hipp operator, and give some definitions of symbols commonly used in this paper. In the third chapter, we consider a Markov adjustment risk model with random dividend strategy. Firstly, we introduce the basic situation of the model, and then use the method of generating function and its inverse transformation, through rigorous mathematical derivation. The recursive formula of Gerber-Shiu function is obtained, and the recurrence formula of ruin probability is obtained. A numerical example is given for a special case. In chapter 4, we consider a risk model of delayed payout with random dividend strategy. By means of generating function and its inverse transformation, we combine the method of mathematics and probability theory with the auxiliary model. The expression of the present value of expected dividend is derived, and a numerical example is obtained when the amount of claim is constant.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F275;F224

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