复合Poisson分布下风险模型及其推广模型的破产概率的研究
发布时间：2019-07-04 10:13
【摘要】：破产理论是风险理论的核心内容。对破产概率及其实际应用的研究有着重要意义。随着风险理论的发展日渐成熟和广泛应用,传统的经典风险模型已经远不能够满足需求,故需要对此模型进行多角度的推广,以便更加接近实际情况。论文从传统的经典风险模型及其推广的基础风险模型出发,结合实际,分别建立了两个新的风险模型,并运用鞅论的方法对新推广的风险模型的破产概率和应用进行研究和总结。论文共分为4章:第一章给出论文的选题背景、意义及应用前景;第二章简略的介绍了一下文中所涉及的一些基本概念和方法;第三章研究了将复合Poisson分布下单一险种的风险模型推广为多险种同时发生赔付的一个风险模型。模型中,保费收入是一个常数,m重险种在同一时刻发生索赔,索赔过程为复合Poisson过程。第四章将Poisson风险模型推广到带干扰的双复合Poisson过程,并对其进行研究。在每个模型中首先分别构造了调节系数所满足的方程,利用函数单调性、凹凸性、极值等证明调节系数唯一且存在,并运用鞅的方法对模型的破产概率和应用进行研究和总结,得到了破产概率的确切表达式,同时推得出Lundberg不等式,并随之给出了关于破产概率的一个极限值。最后对全文进行了综合性的分析,得出全文主要的结论和成果并给出了课题研究的发展方向。
[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.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F840;O211.6
[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.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F840;O211.6
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