分红策略下二元对偶风险模型的研究
发布时间：2018-11-05 19:34
【摘要】：最近几年,随着经济全球化的加剧,来自各个方面的风险越来越趋向复杂和多元化,为此人们越来越关注风险,于是学者们对风险理论特别是破产理论的研究也越来越深层次化。但大多数都是致力于研究保险公司的破产概率、破产时刻、破产前的瞬时盈余等问题,而结合红利策略对红利问题的研究还有待进一步深入。于是本文研究二元对偶风险模型,在分红策略下对直到破产时刻为止红利贴现值的期望的问题,同时考虑红利发放会更加吸引投资者进行投资。所以对二元对偶风险模型下直到破产时刻为止红利贴现值期望的研究具有一定的理论价值和现实指导意义,是一个非常有意义的课题。本文首先介绍了风险理论的一些基本知识和方法；然后考虑到现实中,保险公司会承担不同的保险业务而遇到不同的风险,将一元对偶风险模型推广到独立二元,并加入阈值策略,对破产时刻为止红利贴现值的期望进行了研究,得出它所满足的积分微分方程,同时得出其对应的解析表达式。从理论上并通过数值分析得出在二元的情况下,障碍策略依然是阈值的极限形式。最后又考虑到现实社会中往往不同的风险之间具有一定的关联性,简单的独立二元模型已经不切实际,而且现实中很多外界因素都会对收入产生影响。因此,又在阈值策略下研究了一种收入具有相依关系并由布朗运动驱动的二元对偶风险模型的红利问题,最终得到了这种对偶风险模型下直到破产为止红利贴现值期望的解析表达式。最后,对本文的研究结果作了一个总结,给出了本文的展望。
[Abstract]:In recent years, with the intensification of economic globalization, the risks from various aspects have become more and more complex and diversified, so people are paying more and more attention to the risks. As a result, the study of risk theory, especially bankruptcy theory, is becoming more and more profound. However, most of them are devoted to the study of the bankruptcy probability, the time of bankruptcy, the instantaneous surplus before bankruptcy and so on. However, the study of dividend problem in combination with dividend strategy still needs to be further studied. In this paper, we study the dual risk model, and consider the expectation of the discount value of dividend until the time of bankruptcy under the dividend strategy, and consider that the dividend will attract investors to invest more. Therefore, the research on the expectation of dividend discounted value under the dualistic dual risk model until the time of bankruptcy has certain theoretical value and practical guiding significance, which is a very meaningful topic. This paper first introduces some basic knowledge and methods of risk theory. Then considering the reality, the insurance company will take on different insurance business and encounter different risks. The one-variable dual risk model will be extended to independent duality, and the threshold strategy will be added. In this paper, the expectation of the discount value of the dividend at the ruin time is studied, and the integral differential equation which it satisfies is obtained, and the corresponding analytical expression is obtained. Theoretically and numerically, it is concluded that the barrier strategy is still the limit form of threshold in the case of duality. Finally, considering that there is a certain correlation between different risks in real society, a simple independent binary model is impractical, and a lot of external factors will have an impact on income in reality. Therefore, the dividend problem of a dual risk model with income dependence and driven by Brownian motion is also studied under threshold strategy. Finally, the analytical expression of the expectation of dividend discounted value under the dual risk model is obtained. Finally, the research results of this paper are summarized and the prospect of this paper is given.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O211.67
本文编号：2313156
[Abstract]:In recent years, with the intensification of economic globalization, the risks from various aspects have become more and more complex and diversified, so people are paying more and more attention to the risks. As a result, the study of risk theory, especially bankruptcy theory, is becoming more and more profound. However, most of them are devoted to the study of the bankruptcy probability, the time of bankruptcy, the instantaneous surplus before bankruptcy and so on. However, the study of dividend problem in combination with dividend strategy still needs to be further studied. In this paper, we study the dual risk model, and consider the expectation of the discount value of dividend until the time of bankruptcy under the dividend strategy, and consider that the dividend will attract investors to invest more. Therefore, the research on the expectation of dividend discounted value under the dualistic dual risk model until the time of bankruptcy has certain theoretical value and practical guiding significance, which is a very meaningful topic. This paper first introduces some basic knowledge and methods of risk theory. Then considering the reality, the insurance company will take on different insurance business and encounter different risks. The one-variable dual risk model will be extended to independent duality, and the threshold strategy will be added. In this paper, the expectation of the discount value of the dividend at the ruin time is studied, and the integral differential equation which it satisfies is obtained, and the corresponding analytical expression is obtained. Theoretically and numerically, it is concluded that the barrier strategy is still the limit form of threshold in the case of duality. Finally, considering that there is a certain correlation between different risks in real society, a simple independent binary model is impractical, and a lot of external factors will have an impact on income in reality. Therefore, the dividend problem of a dual risk model with income dependence and driven by Brownian motion is also studied under threshold strategy. Finally, the analytical expression of the expectation of dividend discounted value under the dual risk model is obtained. Finally, the research results of this paper are summarized and the prospect of this paper is given.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O211.67
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