發(fā)布時(shí)間：2018-05-30 23:14

  本文選題：對偶風(fēng)險(xiǎn)模型 + 線性分紅策略��； 參考：《湖南師范大學(xué)》2013年碩士論文

【摘要】：近些年來,在經(jīng)典風(fēng)險(xiǎn)模型研究的基礎(chǔ)上,同時(shí)有不少風(fēng)險(xiǎn)理論界的學(xué)者對它的對偶風(fēng)險(xiǎn)模型產(chǎn)生了興趣.對偶風(fēng)險(xiǎn)模型的應(yīng)用是相當(dāng)普遍的,可以看成是保險(xiǎn)公司、石油公司、科研發(fā)明公司等需要持續(xù)投資且收益不固定的企業(yè).而對于風(fēng)險(xiǎn)模型的研究策略有很多,現(xiàn)在比較熱門的是分紅問題,常見的分紅策略有兩種：一種是常數(shù)門檻策略；另一種是閾紅利邊界策略.然而在實(shí)際生活中,分紅邊界常常是時(shí)刻變化并且依賴于時(shí)間,因而線性邊界更具有實(shí)際意義.具有線性分紅邊界的風(fēng)險(xiǎn)模型最早是由Gerber在1974年提出來,他對經(jīng)典的風(fēng)險(xiǎn)模型作了如下修正：盈余在邊界水平以下時(shí)不發(fā)放紅利；盈余在紅利邊界水平以上時(shí)便發(fā)放紅利,直到發(fā)生下次索賠,如此運(yùn)作的結(jié)果是盈余一旦越過紅利界限便駐留在邊界上.本文的前二章介紹了風(fēng)險(xiǎn)模型的背景及一些基本知識和結(jié)論,本文核心在第三章、第四章以及第五章. 本文第三章討論了對偶風(fēng)險(xiǎn)模型的線性分紅問題,給出了當(dāng)oub時(shí)分紅折現(xiàn)期望值V(u,b)滿足的偏微分積分方程及一些邊界條件；然后介紹矩母函數(shù)M(u,y,b)的定義和性質(zhì),推導(dǎo)出矩母函數(shù)所滿足的偏微分積分方程及邊界條件；最后得到n階分紅折現(xiàn)期望值Vn(u,b)所滿足的偏微分積分方程. 第四章討論了帶干擾的對偶風(fēng)險(xiǎn)模型中的線性分紅,給出了分紅折現(xiàn)期望值V(u,b)、矩母函數(shù)M(u,y,b)和n階分紅折現(xiàn)期望值Vn(u,b)所滿足的偏微分積分方程及邊界條件. 第五章建立了隨機(jī)觀察下的對偶風(fēng)險(xiǎn)模型,給出了折罰函數(shù)mδ(u)所滿足的方程,并且求得當(dāng)密度函數(shù)為指數(shù)分布時(shí)折罰函數(shù)的顯示解.
[Abstract]:In recent years, on the basis of the classical risk model, many scholars in the field of risk theory have been interested in its dual risk model. The application of dual risk model is very common. It can be regarded as insurance company, oil company, scientific research company and so on, which need to invest continuously and the income is not fixed. However, there are a lot of research strategies for risk model, but now the hot problem is dividend. There are two common dividend strategies: one is constant threshold strategy, the other is threshold dividend boundary strategy. However, in real life, the dividend boundary is always changing and dependent on time, so the linear boundary is more practical. The risk model with linear dividend boundary was first put forward by Gerber in 1974. He revised the classical risk model as follows: when the surplus is below the boundary level, it does not pay dividends, and when the surplus is above the dividend boundary level, it pays dividends. Until the next claim occurs, the result of this operation is that the surplus stays at the border once the dividend limit is crossed. The first two chapters of this paper introduce the background of the risk model and some basic knowledge and conclusions. The core of this paper is in the third chapter, the fourth chapter and the fifth chapter. In the third chapter, we discuss the problem of linear dividend for dual risk model, give the partial differential integral equation and some boundary conditions satisfying the expected value of dividend discounted when oub, and then introduce the definition and properties of the moment generating function Mu UU B). The partial differential integral equation satisfied by the moment generating function and the boundary conditions are derived. Finally, the partial differential integral equation satisfied by the expectation value of n order dividend discount is obtained. In chapter 4, we discuss the linear dividend in the dual risk model with disturbance, and give the partial differential integral equations and boundary conditions which are satisfied by the expectation value of dividend discounting, the moment generating function Mnuuyb) and the expectation value of n order dividend. In chapter 5, the dual risk model under random observation is established, the equation satisfied by the penalty function m 未 u) is given, and the explicit solution of the penalty function is obtained when the density function is exponential distribution.
【學(xué)位授予單位】：湖南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：O211.63;F840.3

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本文編號：1957245