随机破产下风险模型的随机分红问题

发布时间：2018-03-25 23:37

本文选题：随机破产　切入点：随机分红　出处：《曲阜师范大学》2017年硕士论文

【摘要】：在经典风险模型理论中,常见分红策略有两种,一种是带壁分红(barrier dividend)策略,即:当盈余超过给定边界b (b 0)时,超出部分当作分红;另一种是阈值分红(threshold dividend)策略,即:当盈余超过b时,超出部分按一定比例当作分红.随着风险理论的不断发展,越来越多的风险模型和理论方法被应用到分红的研究分析中.Albrecher et al. (2011a)考虑了分红时间间隔服从指数分布时,复合泊松风险模型下分红的有关性质.由此我们考虑随机带壁分红策略,即:分红时刻为一随机变量.在分红时刻盈余大于b时超出部分当作分红,若未达到b则不进行分红.经典风险理论中,公司盈余一旦达到负值,便立即宣布破产.而在现实的保险公司运营中即使盈余为负,公司仍有可能继续经营,其破产概率依赖于一个定义在负盈余值上的函数ω(u).随机破产的概念首先由Albrecher et al. (2011b)提出,其研究了随机破产下盈余过程模型为Wiener过程时的随机分红问题.在这篇论文中,我们考虑了两种风险模型在随机破产框架下的随机带壁分红策略的相关问题.论文结构和内容如下:第一章随机破产和随机分红概念介绍及最新的研究进展.第二章研究随机破产下复合泊松风险模型的随机分红问题.第2.1节介绍复合泊松风险模型的概念,叙述一些符号及其定义.第2.2节得到关于期望累计折现分红D(u,b)的积分微分方程,并在一定条件下对方程进行求解.第2.3节在求出最优分红阈值b*的基础上,通过计算得到D(b*,b*)和D'(b*,b*)的一些性质.第2.4节给出一些常见破产率函数求解的例子,进而为2.5节对分段破产率函数近似求解一般破产率函数提供支持,最后在2.6节给出数值模拟,对之前章节得到的结论进行验证和分析.第三章研究随机破产下带扰动复合泊松风险模型的随机分红问题.第3.1节给出风险模型的概念,叙述一些符号及其定义.第3.2节运用和2.2节类似的方法,求出关于期望累计折现分红D(u,b)的积分微分方程.第3.3节在索赔额服从指数分布且ω(u)为常数的条件下,推导出D(u,b)的表达式.第四章对论文进行简要总结.
[Abstract]:In the classical risk model theory, there are two common dividend strategies, one is barrier divider with wall dividend, that is, when the surplus exceeds a given boundary b / b _ 0, the excess is regarded as a dividend, and the other is the threshold dividend threshold divider). That is, when the surplus exceeds b, the excess part is regarded as a dividend in proportion. A growing number of risk models and theoretical methods have been applied to the study and analysis of dividends. Albrecher et al. / 2011a) has taken into account the exponential distribution of dividend interval clothing. Under the compound Poisson risk model, we consider the stochastic wall-walled dividend strategy, that is, the dividend moment is a random variable. When the dividend surplus is greater than b, the excess part is considered as the dividend. In classical risk theory, once a company's surplus reaches a negative value, it is immediately declared bankrupt. In a real insurance company, even if the surplus is negative, it is possible for the company to continue to operate. The ruin probability depends on a function defined on the negative surplus value. The concept of stochastic ruin is first put forward by Albrecher et al. n 2011b. It studies the problem of stochastic dividend when the model of surplus process is Wiener process under stochastic ruin. In this paper, We consider the problems related to the stochastic wall-walled dividend strategy of two risk models under the framework of stochastic ruin. The structure and contents of this paper are as follows: chapter one introduces the concepts of stochastic ruin and stochastic dividend and the latest research progress. In chapter 2, we study the stochastic dividend of compound Poisson risk model under random ruin. Section 2.1 introduces the concept of compound Poisson risk model. Some symbols and their definitions are described. In Section 2.2, an integral differential equation for the expected cumulative discounted dividend is obtained, and the equation is solved under certain conditions. Section 2.3 is based on finding the optimal dividend threshold b *. In section 2.4, some examples of solving the common ruin rate function are given, which support 2.5 section to approximate the general ruin rate function of the piecewise ruin rate function. Finally, the numerical simulation is given in section 2.6. In chapter 3, we study the stochastic dividend problem of perturbed compound Poisson risk model under stochastic ruin. Section 3.1 gives the concept of risk model. Some symbols and their definitions are described. Section 3.2 uses a method similar to section 2.2 to work out an integro-differential equation for the expected cumulative discounted dividend (DUUB). Section 3.3 under the condition that the claimed amount is exponentially distributed and 蠅 u) is constant, The expression of DUUB) is derived. In Chapter 4, the thesis is summarized briefly.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F840

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