本文選題：絕對(duì)破產(chǎn)　切入點(diǎn)：折罰函數(shù)　出處：《湖南師范大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

【摘要】：自從瑞典精算師Filip Lundberg提出復(fù)合泊松風(fēng)險(xiǎn)模型之后,許多學(xué)者通過(guò)放寬關(guān)于索賠時(shí)間和索賠額分布等的假設(shè),將經(jīng)典復(fù)合泊松風(fēng)險(xiǎn)模型進(jìn)行了一些列的推廣,他們主要是計(jì)算最終破產(chǎn)概率,1998年,Gerber-Shiu提出了折罰函數(shù)后,風(fēng)險(xiǎn)理論得到了很大的發(fā)展.本文考慮了在索賠額與索賠來(lái)到時(shí)間具有經(jīng)典FGM Copula相依關(guān)系的復(fù)合泊松風(fēng)險(xiǎn)模型下的絕對(duì)破產(chǎn)問(wèn)題,給出了此模型下Gerber-Shiu折罰函數(shù)的微分積分方程,然后研究了當(dāng)初始值大于0時(shí)絕對(duì)破產(chǎn)折罰函數(shù)的拉普拉普拉斯變換,并在此變換下得到了更新方程,最后給出了在特殊情況下的絕對(duì)破產(chǎn)概率. 本文的第一章主要是介紹風(fēng)險(xiǎn)理論發(fā)展史以及相依風(fēng)險(xiǎn)風(fēng)險(xiǎn)模型的研究現(xiàn)狀和絕對(duì)破產(chǎn)問(wèn)題研究的一些成果.第二章主要給出了本文所用到相關(guān)知識(shí)及模型. 本文核心在第三章和第四章.第三章主要研究了絕對(duì)破產(chǎn)折罰函數(shù)滿足的積分微分方程,并且當(dāng)初始值大于0時(shí),通過(guò)拉普拉斯變換得到了絕對(duì)破產(chǎn)折罰函數(shù)滿足的更新方程,并得到了其解析表達(dá)式.第四章主要研究了在特殊情況下絕對(duì)破產(chǎn)概率的解析表達(dá)式.
[Abstract]:Since the Swedish actuary Filip Lundberg put forward the compound Poisson risk model, many scholars have extended the classical compound Poisson risk model by relaxing the assumptions about the claim time and the distribution of claim amount. In 1998, Gerber-Shiu proposed a penalty function. The risk theory has been greatly developed. In this paper, we consider the absolute ruin problem under the compound Poisson risk model with the classical FGM Copula dependence between the claim amount and the claim arrival time, and give the differential integral equation of the Gerber-Shiu folding function in this model. Then we study the Laplacian transformation of the absolute ruin penalty function when the initial value is greater than 0:00, and obtain the renewal equation under this transformation. Finally, the absolute ruin probability in special cases is given. The first chapter mainly introduces the history of risk theory, the current research situation of dependent risk risk model and some achievements of absolute bankruptcy. The second chapter mainly gives the relevant knowledge and model used in this paper. The core of this paper is in Chapter 3 and Chapter 4th. In Chapter 3, we study the integro-differential equation satisfied by the absolute ruin penalty function, and when the initial value is greater than 0:00, By means of Laplace transformation, the renewal equation of absolute ruin penalty function is obtained, and its analytical expression is obtained. Chapter 4th mainly studies the analytical expression of absolute ruin probability in special cases.
【學(xué)位授予單位】：湖南師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F842;O211.63

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本文編號(hào)：1626375