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  本文選題：復(fù)合Poisson風(fēng)險模型 + 隨機(jī)擾動��； 參考：《遼寧師范大學(xué)》2013年碩士論文

【摘要】：在精算文獻(xiàn)中，復(fù)合Poisson模型是研究得最廣泛的一類更新風(fēng)險過程。目前，復(fù)合Poisson模型有各種推廣形式，，其中復(fù)合復(fù)合Poisson模型（簡記為CCPM）由Minkova（Compound Compound Poisson Risk Model. Serdica Mathematical Journal,35,301-310,2009）最早提出，并研究了該模型的相關(guān)破產(chǎn)問題和再保險問題。受上述文獻(xiàn)啟發(fā)，本文研究幾類廣義的CCPM模型，并對這些模型的破產(chǎn)概率進(jìn)行深入研究。 在第一章中，我們介紹了經(jīng)典的復(fù)合Poisson模型和CCPM的相關(guān)結(jié)果，并且回顧了鞅及布朗運動的相關(guān)概念。第二章我們討論的是保費收入為復(fù)合Poisson過程的CCPM的破產(chǎn)概率。首先，介紹了假設(shè)的合理性，對各個變量賦予相應(yīng)的實際意義。然后我們得到了最終破產(chǎn)概率(u)的表達(dá)形式，并且給出了一個具體實例。第三章是在第二章的基礎(chǔ)上討論了保費收入為復(fù)合Poisson過程帶擾動的CCPM。首先，介紹了模型的結(jié)構(gòu)，最終獲得破產(chǎn)概率滿足的Lundberg型不等式。第四章為了更加貼近保險實踐，討論的是保費收入為雙復(fù)合Poisson過程的CCPM的破產(chǎn)概率。第五章我們考慮對模型進(jìn)行更加深入的拓廣，即假設(shè)保費收入為廣義復(fù)合復(fù)合Poisson過程的CCPM的破產(chǎn)概率。 在本文的證明過程中，共分三個步驟完成這幾類風(fēng)險模型所滿足的Lundberg型不等式。第一步，保證保險公司有正的安全負(fù)載。第二步，對于每種風(fēng)險模型的盈利過程{S t,t0},我們有E(e rSt) e (r)t,分別求出(r)在不同的模型中表達(dá)式，繼而驗證調(diào)節(jié)系數(shù)的存在性。第三步，利用鞅技巧獲得破產(chǎn)概率的上界估計。
[Abstract]:In actuarial literature, compound Poisson model is the most widely studied renewal risk process. At present, the compound Poisson model has various forms of generalization, in which the compound Poisson model (abbreviated as CCPM) is composed of Minkova(Compound Compound Poisson Risk Model.. Serdica Mathematical Journal 35301-310 / 2009 was first put forward, and the related bankruptcy and reinsurance problems of the model were studied. Inspired by the above literatures, this paper studies several generalized CCPM models, and studies the ruin probability of these models. In the first chapter, we introduce the classical composite Poisson model and the related results of CCPM, and review the concepts of martingale and Brownian motion. In chapter 2, we discuss the ruin probability of CCPM in which the premium income is a compound Poisson process. Firstly, the rationality of the hypothesis is introduced, and the corresponding practical significance is given to each variable. Then we obtain the expression of the final ruin probability and give a concrete example. In the third chapter, based on the second chapter, we discuss that the premium income is a complex Poisson process with perturbed CCPM. Firstly, the structure of the model is introduced and the Lundberg type inequality satisfying the ruin probability is obtained. In chapter 4, in order to get closer to the practice of insurance, we discuss the ruin probability of CCPM in which the premium income is a double compound Poisson process. In chapter 5, we consider the further extension of the model, that is, the ruin probability of CCPM assuming that the premium income is a generalized composite Poisson process. In the process of proof in this paper, the Lundberg type inequality satisfied by these risk models is completed in three steps. The first step is to ensure that the insurance company has a positive safety load. In the second step, for the profit process {S t t 0} of each risk model, we have the e rSt. e rSte / rt, respectively, and find out the expressions of r) in different models, and then verify the existence of the adjustment coefficient. In the third step, the upper bound estimate of ruin probability is obtained by using martingale technique.
【學(xué)位授予單位】：遼寧師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F840.4;F224

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 張春生,吳榮;關(guān)于破產(chǎn)概率函數(shù)的可微性的注[J];應(yīng)用概率統(tǒng)計;2001年03期

本文編號：1991160