本文選題：隨機(jī)收入　切入點(diǎn)：地偶風(fēng)險模型　出處：《湖南師范大學(xué)》2013年碩士論文

【摘要】：風(fēng)險理論是精算數(shù)學(xué)的核心內(nèi)容,因此這也引起越來越多從事經(jīng)濟(jì)與保險行業(yè)的研究人員的關(guān)注.眾所周之,經(jīng)典的風(fēng)險模型及其推廣模型主要考慮保費(fèi)收入是連續(xù)的.然而,保費(fèi)連續(xù)性在風(fēng)險模型的應(yīng)用中有很大的局限性.為了使模型更加符合保險公司的實(shí)際運(yùn)作,很多學(xué)者將隨機(jī)收入風(fēng)險模型引入到風(fēng)險理論中.近些年來,保費(fèi)的隨機(jī)化成為風(fēng)險模型研究的熱點(diǎn)課題.本文主要考慮了一類具有隨機(jī)收入風(fēng)險模型的破產(chǎn)相關(guān)問題,并得到了一些相關(guān)結(jié)論.本文的主要結(jié)構(gòu)如下： 第一章,首先,簡單的分析了風(fēng)險問題的研究背景及其最新研究動態(tài).其次,介紹了本文研究的一些破產(chǎn)相關(guān)特征量最后,闡述了本文主要的研究內(nèi)容及其結(jié)論. 第二章,主要介紹了本文所涉及的一些基本知識點(diǎn),同時還簡單的引入了幾類隨機(jī)收入風(fēng)險模型. 第三章,考慮了閾值分紅策略下廣義的Erlang(n)對偶風(fēng)險模型.在經(jīng)典的風(fēng)險模型中,保費(fèi)的收取是連續(xù)的,而索賠過程為復(fù)合Poisson過程.然而在一些公司(藥物的研發(fā)以及石油的開采)實(shí)際運(yùn)作中,用連續(xù)的開銷以及隨機(jī)的收益來描述公司的運(yùn)作則更加符合實(shí)際問題.本章得到了期望折現(xiàn)分紅總量以及破產(chǎn)概率滿足的積分-微分方程及其邊界條件.當(dāng)跳躍的等待時間及其大小分別服從不同參數(shù)的指數(shù)分布時,我們得到了期望折現(xiàn)分紅總量與破產(chǎn)概率的顯示解析式.同時,在給定一些參數(shù)的具體數(shù)值情況下,求出了期望折現(xiàn)分紅總量與破產(chǎn)概率的數(shù)值表達(dá)式. 第四章,主要考慮了由布朗運(yùn)動擾動的隨機(jī)收入風(fēng)險模型,假定隨機(jī)保費(fèi)收益過程以及隨機(jī)索賠過程分別為Poisson過程與廣義的Erla-ng(n)過程且單個保費(fèi)收益的大小是服從參數(shù)為β-1的指數(shù)分布.通過計(jì)算推導(dǎo)出Gerber-Shiu折罰函數(shù)的拉普拉斯變換的顯示表達(dá)式,最后運(yùn)用拉格朗日差值公式得到了折罰函數(shù)的漸近表達(dá)式及其數(shù)值解.
[Abstract]:Risk theory is the core of actuarial mathematics, so more and more researchers engaged in economics and insurance industry pay attention to it.As we all know, the classical risk model and its extension model mainly consider that premium income is continuous.However, premium continuity has great limitations in the application of risk model.In order to make the model more in line with the actual operation of insurance companies, many scholars introduce the stochastic income risk model into the risk theory.In recent years, the randomization of premium is a hot topic in risk model research.In this paper, we consider the ruin problems of a class of stochastic income risk models and obtain some relevant conclusions.The main structure of this paper is as follows:In the first chapter, the research background and the latest research trends of the risk problem are briefly analyzed.Secondly, the paper introduces some characteristic quantities of bankruptcy. Finally, the main contents and conclusions of this paper are described.The second chapter mainly introduces some basic knowledge of this paper, and introduces several kinds of stochastic income risk models.In chapter 3, we consider the generalized Erlangn) dual risk model under threshold dividend strategy.In the classical risk model, the premium collection is continuous, while the claim process is a compound Poisson process.However, in the actual operation of some companies (drug research and development and oil extraction), it is more realistic to describe the company's operation with continuous expenses and random income.In this chapter, we obtain the integro-differential equations and boundary conditions of the total expected discounted dividends and the ruin probability.When the waiting time and the size of the hopping are obtained from the exponential distribution of different parameters, we obtain the expression of the total expected discounted dividend and the ruin probability.At the same time, the numerical expressions of the total amount of expected discounted dividends and the ruin probability are obtained under the condition of given the specific values of some parameters.In chapter 4, the stochastic income risk model, which is disturbed by Brownian motion, is considered.The stochastic premium return process and the stochastic claim process are assumed to be Poisson processes and generalized Erla-ngn processes, respectively, and the size of a single premium income is an exponential distribution with a parameter of 尾 -1.The display expression of Laplace transform of Gerber-Shiu penalty function is deduced by calculation. Finally, the asymptotic expression of penalty function and its numerical solution are obtained by using Lagrange difference formula.
【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】：O211.6;F840.3

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 ;Constant Barrier Strategies in a Two-state Markov-modulated Dual Risk Model[J];Acta Mathematicae Applicatae Sinica(English Series);2011年04期

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本文編號：1706038