带扰动常利率对偶风险模型的分红问题研究

发布时间：2018-01-15 01:25

本文关键词：带扰动常利率对偶风险模型的分红问题研究　出处：《曲阜师范大学》2013年硕士论文　论文类型：学位论文

【摘要】：在精算数学中,对经典风险模型下的最优分红问题己经进行了研究.但是随着金融业务和保险公司业务的发展,经典风险模型的对偶模型越来越受到重视.文献[42]主要研究了带利率和常数红利边界的对偶风险模型,给出了收益服从指数分布时,总红利现值的期望V(u;b)和总红利现值的n阶矩Vn(u；b)的表达式.本文在此基础上加入了布朗运动干扰,主要研究带扰动的常利率对偶风险模型的分红问题. 本文一共分四章. 第一章主要介绍了对偶风险模型的研究历史和现状,给出了本文中用到的符号和公式,并解释它们所表示的意义. 第二章主要研究了带扰动的常利率对偶风险模型的障碍分红问题.我们分别研究总红利现值的期望V(u；b)和总红利现值的矩母函数M(u,y；b),并得到了它们满足的积分-微分方程,主要结果如下：定理1总红利现值的期望V(u,b)满足如下积分-微分方程定理2总红利现值的矩母函数M(u,y；b)满足如下积分-微分方程第三章主要研究了带扰动的常利率对偶风险模型的阈值分红问题.我们分别研究总红利现值的期望和总红利现值的矩母函数,得到它们满足的积分-微分方程,主要结果如下：定理3总红利现值的期望V(u；b)满足如下积分-微分方程其中定理4总红利现值的矩母函数M(u,y;b)满足如下积分-微分方程其中第四章主要研究了带扰动的常利率对偶风险模型在阂值分红策略下的罚金折现期望函数,得到了m(u;b)满足的积分-微分方程,主要结果如下：定理5罚金折现期望函数m(u;b)满足如下积分-微分方程其中
[Abstract]:In Actuarial Mathematics, the optimal dividend problem for classical risk model has been studied. But with the development of financial business and the business of insurance companies, and the dual model of the classical risk model more attention. The [42] mainly studies the dual risk model with interest rate and constant dividend income, given the exponential distribution when the total present value of dividends expected V (U; b) n moment Vn and the total present value of dividends (U; b). The expression on the basis of joining Brown motion interference, mainly studies the dividend problem with perturbation interest dual risk model.
This article is divided into four chapters.
In the first chapter, the history and present situation of the dual risk model are introduced, and the symbols and formulas used in this paper are given, and the meaning expressed by them is explained.
In the second chapter, we mainly study the barrier dividend problem of the constant interest rate dual risk model with perturbation. We study the expectation function V (U, b) of the total dividend and the moment generating function M (U, y, b) of the total dividend present value, and get the integral differential equation that they satisfy.
The expectation V (U, b) of the present value of the total dividend of Theorem 1 satisfies the following integral differential equation
The moment mother function M (U, y; b) of the present value of the total dividend of theorem 2 satisfies the following integral differential equation
The third chapter mainly studies the threshold dividend problem of the duer risk model with perturbed constant interest rate. We study the expectation function of the total dividend and the moment generating function of the total dividend value, and get the integral differential equation which satisfies them. The main results are as follows.
The expectation V (U; b) of the present value of the total dividend of Theorem 3 satisfies the following integral differential equation
The moment mother function M (U, y; b) of the present value of the total dividend of Theorem 4 satisfies the following integral differential equation
The fourth chapter mainly studies the dual risk model with constant interest perturbation value of the expected discounted penalty function in the threshold dividend strategy, the M (U; b) satisfies the Integro differential equation, the main results are as follows: Theorem 5 expected discounted penalty function m (U; b) to meet the following Integro differential equation
among

【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】：F830;O211.6

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