具有Parisian延迟分红的对偶风险模型

发布时间：2018-05-15 06:33

本文选题：对偶风险模型 + Parisian延迟　；参考：《曲阜师范大学》2017年硕士论文

【摘要】：在关于破产问题的论文中,一般习惯作直接性的评价.例如,关于破产时刻的确定,当盈余过程达到一个负值时就立刻宣布破产;另一方面是关于分红支付的确定.通常的分红是当盈余过程超过一个特定的临界值时,分红就会发生.但是,从实际的角度来看,这种决策制定的体制是不太合理的.为了解决这个问题,一些学者引入了金融学中的“Parisian延迟”的概念.因“Parisian延迟”允许决策的执行有一定的延期,所以使得破产理论中的一些概念更加贴近现实.Parisian概念一般被用到以下两个不同的方面.一方面把“Parisian延迟”应用于破产,从而得到Parisian破产时间.在这种定义下,只有当盈余过程连续为负值的时间超过规定时间,才考虑宣布破产.另一方面把“Parisian延迟”应用于分红,引出了 Parisian分红时间.在这种定义下,只有盈余过程连续地在一特定的临界值之上的时间超过规定时间,才考虑进行分红.本论文研究的主要问题是:对偶风险模型的首次Parisian分红时间及对偶风险模型在破产前进行Parisian分红的问题.本论文的结构如下:第一章是绪论及模型介绍.这一章分为三部分,第一部分主要介绍了对偶风险模型及“Parisian延迟”的发展历程;其余两部分分别介绍了经典风险模型以及对偶风险模型.第二章分析了经典风险模型与对偶风险模型之间的关系并通过经典风险模型的Parisian破产时间的Laplace变换给出了对偶风险模型的首次Parisian分红时间的Laplace 变换.第三章分为两个部分,分别从两个角度研究了对偶风险模型在破产前进行Parisian分红的概率.第一部分,给出一个破产概率的广义的矩母函数hd(u).不难发现,当r=1,δ=0时,hd(u)为初值为u的对偶风险模型在Parisian分红前破产的概率,而1 - hd(u)为对偶风险模型在破产前进行Parisian分红的概率.在论文中得到了hd(u)所满足的积分微分方程以及当收入分布为指数分布或混合指数分布时,hd(u)的表达式;第二部分我们从另一个方面考虑,给出了首次Parisian延迟分红时刻的矩母函数Vδ(u; b).当δ = 0时,Vδ(u;b)为初值为u的对偶风险模型在破产前进行Parisian分红的概率.同样地,得到了Vδ(u;b)所满足的积分微分方程以及当收入分布为指数分布或混合指数分布时,Vδ(u;b)的表达式.
[Abstract]:In the papers on bankruptcy, the general custom is to make a direct assessment. For example, with regard to the determination of the time of bankruptcy, bankruptcy is declared immediately when the surplus process reaches a negative value; on the other hand, the determination of dividend payments. The usual dividend is when the surplus process exceeds a specific threshold, the dividend occurs. However, from a practical point of view, this system of decision-making is not very reasonable. To solve this problem, some scholars have introduced the concept of "Parisian delay" in finance. Because "Parisian delay" allows decision execution to be delayed to some extent, some concepts in bankruptcy theory are generally used in the following two different aspects. On the one hand, the "Parisian delay" is applied to the bankruptcy to obtain the Parisian bankruptcy time. Under this definition, a bankruptcy declaration is considered only if the surplus process continues to be negative for longer than the specified time. On the other hand, the Parisian delay is applied to the dividend, which leads to the Parisian dividend time. Under this definition, dividends are considered only if the surplus process continuously exceeds a specified critical value for a specified period of time. The main problems of this thesis are: the first Parisian dividend time of dual risk model and the Parisian dividend of dual risk model before bankruptcy. The structure of this thesis is as follows: the first chapter is introduction and model introduction. This chapter is divided into three parts. The first part mainly introduces the dual risk model and the development of "Parisian delay", and the other two parts introduce the classical risk model and dual risk model respectively. In chapter 2, the relationship between the classical risk model and the dual risk model is analyzed, and the Laplace transformation of the first Parisian dividend time of the dual risk model is given by the Laplace transformation of the Parisian ruin time of the classical risk model. The third chapter is divided into two parts. We study the probability of Parisian dividend in dual risk model before bankruptcy from two angles. In the first part, a generalized moment generating function of ruin probability is given. It is not difficult to find that the dual risk model with initial value u is the probability of ruin before the Parisian dividend, and the dual risk model is the probability of Parisian dividend before the ruin of the dual risk model when r = 1, 未 = 0. In this paper, we obtain the expression of the integro-differential equation satisfied by hddu) and the expression of the income distribution when the income distribution is exponential distribution or mixed exponential distribution. In the second part, we consider another aspect. In this paper, the moment generating function of the first Parisian delay dividend moment is given. When 未 = 0, the probability of Parisian dividend is obtained for the dual risk model with initial value of u when 未 = 0. Similarly, the integro-differential equations satisfied by V 未 U B) and the expressions of V 未 u B) when the income distribution is exponential distribution or mixed exponential distribution are obtained.
【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;F272

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