本文關(guān)鍵詞：帶擾動(dòng)常利率對(duì)偶風(fēng)險(xiǎn)模型的分紅問(wèn)題研究　出處：《曲阜師范大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

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【摘要】：在精算數(shù)學(xué)中,對(duì)經(jīng)典風(fēng)險(xiǎn)模型下的最優(yōu)分紅問(wèn)題己經(jīng)進(jìn)行了研究.但是隨著金融業(yè)務(wù)和保險(xiǎn)公司業(yè)務(wù)的發(fā)展,經(jīng)典風(fēng)險(xiǎn)模型的對(duì)偶模型越來(lái)越受到重視.文獻(xiàn)[42]主要研究了帶利率和常數(shù)紅利邊界的對(duì)偶風(fēng)險(xiǎn)模型,給出了收益服從指數(shù)分布時(shí),總紅利現(xiàn)值的期望V(u;b)和總紅利現(xiàn)值的n階矩Vn(u；b)的表達(dá)式.本文在此基礎(chǔ)上加入了布朗運(yùn)動(dòng)干擾,主要研究帶擾動(dòng)的常利率對(duì)偶風(fēng)險(xiǎn)模型的分紅問(wèn)題. 本文一共分四章. 第一章主要介紹了對(duì)偶風(fēng)險(xiǎn)模型的研究歷史和現(xiàn)狀,給出了本文中用到的符號(hào)和公式,并解釋它們所表示的意義. 第二章主要研究了帶擾動(dòng)的常利率對(duì)偶風(fēng)險(xiǎn)模型的障礙分紅問(wèn)題.我們分別研究總紅利現(xiàn)值的期望V(u；b)和總紅利現(xiàn)值的矩母函數(shù)M(u,y；b),并得到了它們滿足的積分-微分方程,主要結(jié)果如下： 定理1總紅利現(xiàn)值的期望V(u,b)滿足如下積分-微分方程 定理2總紅利現(xiàn)值的矩母函數(shù)M(u,y；b)滿足如下積分-微分方程 第三章主要研究了帶擾動(dòng)的常利率對(duì)偶風(fēng)險(xiǎn)模型的閾值分紅問(wèn)題.我們分別研究總紅利現(xiàn)值的期望和總紅利現(xiàn)值的矩母函數(shù),得到它們滿足的積分-微分方程,主要結(jié)果如下： 定理3總紅利現(xiàn)值的期望V(u；b)滿足如下積分-微分方程 其中定理4總紅利現(xiàn)值的矩母函數(shù)M(u,y;b)滿足如下積分-微分方程其中 第四章主要研究了帶擾動(dòng)的常利率對(duì)偶風(fēng)險(xiǎn)模型在閡值分紅策略下的罰金折現(xiàn)期望函數(shù),得到了m(u;b)滿足的積分-微分方程,主要結(jié)果如下：定理5罰金折現(xiàn)期望函數(shù)m(u;b)滿足如下積分-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

【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F830;O211.6

【參考文獻(xiàn)】

相關(guān)期刊論文 前3條

1 徐俊科;劉再明;宋華;;一類帶投資收益風(fēng)險(xiǎn)模型的罰金折現(xiàn)期望[J];經(jīng)濟(jì)數(shù)學(xué);2007年03期

2 袁海麗;胡亦鈞;;帶利率和常數(shù)紅利邊界的對(duì)偶風(fēng)險(xiǎn)模型的研究[J];數(shù)學(xué)學(xué)報(bào);2012年01期

3 ;Some Results for the Compound Poisson Process That Is Perturbed by Diffusion[J];Acta Mathematicae Applicatae Sinica(English Series);2002年01期

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本文編號(hào)：1426185