本文選題：復合泊松風險模型　切入點：Gerber-Shiu函數(shù)　出處：《曲阜師范大學》2014年碩士論文

【摘要】：近幾十年來,關于帶有隨機利率的擾動經(jīng)典風險模型的研究取得較好的成果.Gerber and Yang (2007)研究了帶有投資的擾動風險模型的絕對破產(chǎn)問題,并討論了當索賠服從指數(shù)分布的絕對破產(chǎn)概率問題；Yin and Wen (2013)對Paulsen and Gjessing (1997a)中的模型進行了拓展,將隨機利率和經(jīng)典模型中的索賠的取值范圍設為(-∞,∞),并且研究了該模型的矩母函數(shù)和分紅問題. 在這篇論文中,我們仍然假設索賠量與索賠來到時刻是相互獨立的.兩個相關的布朗運動分別影響著盈余過程和投資收入過程.然而當盈余為負數(shù)的時候,保險公司以常數(shù)利率貸款從而保持正常運營；當盈余為正時,保險公司按照一定的比例進行兩種投資：有風險的和無風險的投資；當盈余達到一個常數(shù)界限時,保險公司為了爭取到更多的客戶,按照某種策略進行分紅.近年來,關于投資收入、貸款和分紅的問題吸引著人們大量關注. 這篇論文就是在帶有隨機利率的經(jīng)典復合泊松模型中,提出了按常值紅利界限分紅,研究了絕對破產(chǎn)條件下同時帶有風險投資和無風險投資的經(jīng)典風險模型,該模型中的索賠{Xi}是相互獨立的隨機變量序列,并且是取值在(0,∞)上,得至Gerber-Shiu函數(shù)的積分微分方程,由于直接解出帶參數(shù)的二階積分微分方程是有困難的,本文只給出σ12a=2,λ=0,ω(x,y)=l時的二階微分方程：和它們的解分別為 本文還分別討論了該風險模型的障礙分紅和閾值分紅策略下的期望折扣分紅函數(shù)的積分微分方程與矩母函數(shù)的積分微分方程,在例題中給出密度函數(shù)為p(x)=e-x,x∈(0,∞)上的障礙分紅方程,且解出當σ12a3=2,δ=b2=0,λ=a+c時分紅方程的解的表達式；在閾值分紅中,給出σ12a=2,λ=0時的解. 本論文結構如下：第一章緒論是對本文主要結果的簡單介紹；第二章對本文所討論的風險模型進行了推導,論證和介紹；第三章推導出Gerber-Shiu函數(shù)的積分微分方程,找到方程滿足的邊界條件,給出特殊情形下方程的解并找到常數(shù)系數(shù)的確切表達式；第四和第五章是障礙分紅和閾值分紅策略的期望折扣分紅函數(shù)的積分微分方程,同樣找到方程的邊界條件并得到特殊情況下的一些結果.
[Abstract]:In recent years, about.Gerber and Yang achieved good results of disturbance of the classical risk model with stochastic interest rate (2007) of the perturbed risk model with investment absolute ruin, and discussed when the claim is exponential absolute ruin probability distribution problem; Yin and Wen (2013) Paulsen and Gjessing (1997A) in the model, the stochastic interest rate and the classical model in the range of claims for (- OO, OO), and studied the model of the moment generating function and dividend problem.
In this paper, we will assume the claim amount and the arrival times are independent of each other. Two related Brown movement affects the surplus process and investment income. However, when the surplus is negative, the insurance company with constant interest rate loans to maintain normal operation; when the surplus is positive, the insurance company two kinds of investment in a certain proportion: risk and non risk investment; when the surplus reaches a constant threshold, the insurance company in order to get more customers, dividends in accordance with a certain strategy. In recent years, the investment income, loan and dividend problem attracts people a lot of attention.
This paper is in the classical compound Poisson model with stochastic interest rates, according to the constant dividend barrier dividend, the classical risk model is studied under the condition of absolute ruin with risk investment and risk investment, this model claims {Xi} is independent of the random variable sequence, and the value is in (0 infinity), too, Integro differential equations to Gerber-Shiu function, the direct solution of Two Order Integro differential equations with parameters is difficult, this paper only gives a 12a=2, a =0 (x, y), Omega two order differential equation: =l and their solutions respectively.
This paper discussed the integral differential equations with integral differential equation and moment generating function of the expected discounted dividends function of the risk model with threshold dividend strategy and dividend barrier under the, in the examples given in the density function p (x) =e-x, X (0, OO) barrier equation, and the solution of the sigma Delta 12a3=2, =b2=0, expressions of dividend equation lambda =a+c; the threshold dividend, given a 12a=2, a =0 solution.
This paper is structured as follows: the first chapter is a brief introduction of the main results of this paper; the second chapter discussed the risk model of the derivation, demonstration and introduction; third chapter derived the Integro differential equations of Gerber-Shiu function, find the equation of boundary condition equation solutions under special conditions and find the exact constant expression the coefficient of fourth; and the fifth chapter is the Integro differential equations of the expected discounted dividends function barrier and threshold dividend strategy, also find the boundary conditions of the equations and obtain some results under special circumstances.

【學位授予單位】：曲阜師范大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：F842.3;F832.4;O211.6

【參考文獻】

相關期刊論文 前1條

1 丁芳清;姚定俊;;常利息力影響下跳擴散模型的分紅問題(英文)[J];應用概率統(tǒng)計;2011年02期

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本文編號：1721364