【摘要】：破產(chǎn)理論是風(fēng)險(xiǎn)理論的核心內(nèi)容。對破產(chǎn)概率及其實(shí)際應(yīng)用的研究有著重要意義。隨著風(fēng)險(xiǎn)理論的發(fā)展日漸成熟和廣泛應(yīng)用,傳統(tǒng)的經(jīng)典風(fēng)險(xiǎn)模型已經(jīng)遠(yuǎn)不能夠滿足需求,故需要對此模型進(jìn)行多角度的推廣,以便更加接近實(shí)際情況。論文從傳統(tǒng)的經(jīng)典風(fēng)險(xiǎn)模型及其推廣的基礎(chǔ)風(fēng)險(xiǎn)模型出發(fā),結(jié)合實(shí)際,分別建立了兩個(gè)新的風(fēng)險(xiǎn)模型,并運(yùn)用鞅論的方法對新推廣的風(fēng)險(xiǎn)模型的破產(chǎn)概率和應(yīng)用進(jìn)行研究和總結(jié)。論文共分為4章:第一章給出論文的選題背景、意義及應(yīng)用前景;第二章簡略的介紹了一下文中所涉及的一些基本概念和方法;第三章研究了將復(fù)合Poisson分布下單一險(xiǎn)種的風(fēng)險(xiǎn)模型推廣為多險(xiǎn)種同時(shí)發(fā)生賠付的一個(gè)風(fēng)險(xiǎn)模型。模型中,保費(fèi)收入是一個(gè)常數(shù),m重險(xiǎn)種在同一時(shí)刻發(fā)生索賠,索賠過程為復(fù)合Poisson過程。第四章將Poisson風(fēng)險(xiǎn)模型推廣到帶干擾的雙復(fù)合Poisson過程,并對其進(jìn)行研究。在每個(gè)模型中首先分別構(gòu)造了調(diào)節(jié)系數(shù)所滿足的方程,利用函數(shù)單調(diào)性、凹凸性、極值等證明調(diào)節(jié)系數(shù)唯一且存在,并運(yùn)用鞅的方法對模型的破產(chǎn)概率和應(yīng)用進(jìn)行研究和總結(jié),得到了破產(chǎn)概率的確切表達(dá)式,同時(shí)推得出Lundberg不等式,并隨之給出了關(guān)于破產(chǎn)概率的一個(gè)極限值。最后對全文進(jìn)行了綜合性的分析,得出全文主要的結(jié)論和成果并給出了課題研究的發(fā)展方向。
[Abstract]:Bankruptcy theory is the core content of risk theory. It is of great significance to study the ruin probability and its practical application. With the development and wide application of risk theory, the traditional classical risk model is far from meeting the demand, so it is necessary to popularize the model from many angles in order to be closer to the actual situation. Based on the traditional classical risk model and its extended basic risk model, two new risk models are established in this paper, and the ruin probability and application of the newly extended risk model are studied and summarized by using martingale theory. The paper is divided into four chapters: the first chapter gives the background, significance and application prospect of the paper; the second chapter briefly introduces some basic concepts and methods involved in this paper; in the third chapter, the risk model of single insurance type under compound Poisson distribution is extended to a risk model of multiple insurance types at the same time. In the model, the premium income is a constant, the m heavy insurance type claims at the same time, and the claim process is a compound Poisson process. In chapter 4, the Poisson risk model is extended to the double compound Poisson process with interference, and its research is carried out. In each model, the equations satisfied by the adjustment coefficient are constructed respectively, and the function monotonicity, concavity and convexity, extreme value and so on are used to prove the uniqueness and existence of the adjustment coefficient. The ruin probability and application of the model are studied and summarized by using the martingale method, and the exact expression of the ruin probability is obtained. At the same time, the Lundberg inequality is derived, and then a limit value about the ruin probability is given. Finally, a comprehensive analysis of the full text is carried out, the main conclusions and results of the full text are obtained, and the development direction of the subject research is given.
【學(xué)位授予單位】：渤海大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F840;O211.6

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本文編號：2509845