【摘要】：破產(chǎn)理論是風險理論的核心內(nèi)容。對破產(chǎn)概率及其實際應用的研究有著重要意義。隨著風險理論的發(fā)展日漸成熟和廣泛應用,傳統(tǒng)的經(jīng)典風險模型已經(jīng)遠不能夠滿足需求,故需要對此模型進行多角度的推廣,以便更加接近實際情況。論文從傳統(tǒng)的經(jīng)典風險模型及其推廣的基礎風險模型出發(fā),結合實際,分別建立了兩個新的風險模型,并運用鞅論的方法對新推廣的風險模型的破產(chǎn)概率和應用進行研究和總結。論文共分為4章:第一章給出論文的選題背景、意義及應用前景;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;第三章研究了將復合Poisson分布下單一險種的風險模型推廣為多險種同時發(fā)生賠付的一個風險模型。模型中,保費收入是一個常數(shù),m重險種在同一時刻發(fā)生索賠,索賠過程為復合Poisson過程。第四章將Poisson風險模型推廣到帶干擾的雙復合Poisson過程,并對其進行研究。在每個模型中首先分別構造了調(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,并運用鞅的方法對模型的破產(chǎn)概率和應用進行研究和總結,得到了破產(chǎn)概率的確切表達式,同時推得出Lundberg不等式,并隨之給出了關于破產(chǎn)概率的一個極限值。最后對全文進行了綜合性的分析,得出全文主要的結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.
【學位授予單位】：渤海大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：F840;O211.6

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