随机利率下带干扰的对偶风险模型的分红问题
发布时间：2018-11-22 12:04
【摘要】：1957年分红问题被De Finetti在离散时间模型中讨论过之后,分红问题成为保险精算研究的一个重要课题,大量著作开始研究分红问题.很多模型中的分红问题已经被研究的非常透彻,也得到了切实可行的结果.然而随着社会的发展和时代的变迁,人们考虑问题的多元化,对偶风险模型受到了越来越多专家学者的青睐.本文将在前人的基础之上,在一般的对偶风险模型中,加入随机利率的投资和干扰项,研究在这些条件下的Barrier分红策略和Threshold分红策略.根据研究内容,本文可分为三章： 第一章为绪论.这一部分简要介绍了对偶模型以及分红问题的背景,为下面的研究做准备. 第二章讨论了Barrier分红策略.研究了到破产为止的总红利折现D的矩母函数及n阶矩满足的积分-微分方程及方程满足的边界条件,并将结果与前人的结果进行对比.特别求出了总红利现值期望V(u；b)满足的积分-微分方程和方程满足的边界条件. 第三章是第二章的推广,讨论了在Threshold策略下的分红问题.研究了到破产为止的总红利折现D的矩母函数及n阶矩满足的积分-微分方程及方程满足的边界条件,并将结果与前人的结果进行对比.特别求出了总红利现值期望V(u；b)满足的积分-微分方程和方程满足的边界条件.
[Abstract]:After the dividend problem was discussed by De Finetti in the discrete time model in 1957, the dividend problem became an important subject in the actuarial study of insurance, and a large number of works began to study the dividend problem. The dividend problem in many models has been studied very thoroughly and got practical results. However, with the development of society and the change of times, people consider the diversification of the problem, dual risk model is more and more favored by experts and scholars. In this paper, on the basis of previous studies, we will add the investment and interference terms of stochastic interest rate to the general dual risk model, and study the Barrier dividend strategy and the Threshold dividend strategy under these conditions. According to the research content, this paper can be divided into three chapters: the first chapter is an introduction. This part briefly introduces the dual model and the background of dividend problem, and prepares for the following research. The second chapter discusses the Barrier dividend strategy. In this paper, we study the moment generating function of the total dividend discounted D and the boundary conditions of the integro-differential equation and the equation satisfied by the n-order moments, and compare the results with the previous ones. In particular, the boundary conditions of integro-differential equations and equations satisfying the expected present value of total dividend V (UB) are obtained. The third chapter is the generalization of chapter 2, and discusses the dividend problem under Threshold strategy. In this paper, we study the moment generating function of the total dividend discounted D and the boundary conditions of the integro-differential equation and the equation satisfied by the n-order moments, and compare the results with the previous ones. In particular, the boundary conditions of integro-differential equations and equations satisfying the expected present value of total dividend V (UB) 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】：2013
【分类号】：O211.63;F840.3
本文编号：2349335
[Abstract]:After the dividend problem was discussed by De Finetti in the discrete time model in 1957, the dividend problem became an important subject in the actuarial study of insurance, and a large number of works began to study the dividend problem. The dividend problem in many models has been studied very thoroughly and got practical results. However, with the development of society and the change of times, people consider the diversification of the problem, dual risk model is more and more favored by experts and scholars. In this paper, on the basis of previous studies, we will add the investment and interference terms of stochastic interest rate to the general dual risk model, and study the Barrier dividend strategy and the Threshold dividend strategy under these conditions. According to the research content, this paper can be divided into three chapters: the first chapter is an introduction. This part briefly introduces the dual model and the background of dividend problem, and prepares for the following research. The second chapter discusses the Barrier dividend strategy. In this paper, we study the moment generating function of the total dividend discounted D and the boundary conditions of the integro-differential equation and the equation satisfied by the n-order moments, and compare the results with the previous ones. In particular, the boundary conditions of integro-differential equations and equations satisfying the expected present value of total dividend V (UB) are obtained. The third chapter is the generalization of chapter 2, and discusses the dividend problem under Threshold strategy. In this paper, we study the moment generating function of the total dividend discounted D and the boundary conditions of the integro-differential equation and the equation satisfied by the n-order moments, and compare the results with the previous ones. In particular, the boundary conditions of integro-differential equations and equations satisfying the expected present value of total dividend V (UB) 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】：2013
【分类号】：O211.63;F840.3
【参考文献】
中国期刊全文数据库 前1条
1 袁海丽;胡亦钧;;带利率和常数红利边界的对偶风险模型的研究[J];数学学报;2012年01期
，本文编号：2349335
本文链接：https://www.wllwen.com/jingjilunwen/bxjjlw/2349335.html
