隨機利率下帶干擾的對偶風險模型的分紅問題
發(fā)布時間：2018-11-22 12:04
【摘要】：1957年分紅問題被De Finetti在離散時間模型中討論過之后,分紅問題成為保險精算研究的一個重要課題,大量著作開始研究分紅問題.很多模型中的分紅問題已經(jīng)被研究的非常透徹,也得到了切實可行的結果.然而隨著社會的發(fā)展和時代的變遷,人們考慮問題的多元化,對偶風險模型受到了越來越多專家學者的青睞.本文將在前人的基礎之上,在一般的對偶風險模型中,加入隨機利率的投資和干擾項,研究在這些條件下的Barrier分紅策略和Threshold分紅策略.根據(jù)研究內(nèi)容,本文可分為三章： 第一章為緒論.這一部分簡要介紹了對偶模型以及分紅問題的背景,為下面的研究做準備. 第二章討論了Barrier分紅策略.研究了到破產(chǎn)為止的總紅利折現(xiàn)D的矩母函數(shù)及n階矩滿足的積分-微分方程及方程滿足的邊界條件,并將結果與前人的結果進行對比.特別求出了總紅利現(xiàn)值期望V(u；b)滿足的積分-微分方程和方程滿足的邊界條件. 第三章是第二章的推廣,討論了在Threshold策略下的分紅問題.研究了到破產(chǎn)為止的總紅利折現(xiàn)D的矩母函數(shù)及n階矩滿足的積分-微分方程及方程滿足的邊界條件,并將結果與前人的結果進行對比.特別求出了總紅利現(xiàn)值期望V(u；b)滿足的積分-微分方程和方程滿足的邊界條件.
[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.
【學位授予單位】：曲阜師范大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：O211.63;F840.3
本文編號：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.
【學位授予單位】：曲阜師范大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：O211.63;F840.3
【參考文獻】
中國期刊全文數(shù)據(jù)庫 前1條
1 袁海麗;胡亦鈞;;帶利率和常數(shù)紅利邊界的對偶風險模型的研究[J];數(shù)學學報;2012年01期
，本文編號：2349335
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