【作者】 方汶铭；

【导师】 王永茂；

【作者基本信息】 燕山大学 ， 概率论与数理统计， 2009， 硕士

【摘要】 风险理论是近代数学的一个重要分支,主要应用于金融、保险、证券投资以及风险管理等方面,也是当今精算界和数学界研究的热门课题。本文主要研究了几类不同索赔情形下风险模型的破产概率及保险风险证券化问题。全文共分为五章。第一章介绍了破产理论和保险风险证券化的发展史及现状,并在经典风险模型的基础上,介绍了研究破产概率时可以拓展的一些方向,最后给出了本文研究过程中所用到的重要方法、主要结果和创新点。第二章在Cramèr-Lundberg经典风险模型的基础上,把个体索赔额服从混合指数分布( k = 2)时最终破产概率显式解的结论推广到索赔额服从一般混合指数分布(k = n)的情形。第三章研究了在重尾索赔下延迟更新风险模型中破产概率的一个局部等价式,并修正了已有文献[53]证明中的漏洞。第四章研究了一类带有投资回报的离散时间风险模型,运用递归法得到了一个重尾损失情形下有限时间破产概率的渐进式,是Tang、Tsitsiashvili研究的一个有益扩展。第五章根据我国是巨灾高发区的实际情况,讨论了在我国实行保险风险证券化的必要性和可行性,并提出了若干建议。更多还原

【Abstract】 Risk theory is an important branch of modern mathematics, which is mainly applied in finance, insurance, securities investment and the risk management. Nowadays, the collective risk theory is one of the most intriguing fields both in actuarial and mathematical science.The paper focuses on the ruin probabilities of risk model under several types of circumstances where claim is lodged and the securitization of insurance risk.The paper consists of five chapters. Chapter 1 introduces the developme -nt and the state of art of the insurance ruin theory and securitization of insurance risk. On the basis of the classical risk model, some new research areas are presented. At the same time, research methods, important findings and innovative points are given as well.In Chapter 2, according to the classical risk model proposed by Cramèr- Lundberg, the explicit solution of the ultimate ruin probability of the claims having mixed exponential distribution ( k = 2) is extended to the situation where the claims have general mixed exponential distribution ( k = n).Chapter 3 investigates asympototic ruin probabilities of the delayed renewal risk model with heavy-tailed claims, and also revises a pitfall relations -hip in the formula derivation of the 53rd literature.In Chapter 4, a discrete time risk model with investment return is studied. An asympototica for the finite time ruin probability under subexponent -ial loss is obtained by the inductive method, which is a beneficial extension to the results of Tang and Tsitsiashvili.In Chapter 5, since our country is highly vulnerable to catastrophe, the need and feasibility of implementing the securitization of insurance risk is investigated, and some reasonable suggestions are proposed as well.更多还原