两类延迟更新风险模型破产概率及其渐近解研究
发布时间：2018-10-08 06:28
【摘要】：风险理论研究的核心问题就是保险公司的破产概率，由于重尾分布可以很好地用来刻画金融保险业中的极端事件，因此索赔额服从重尾分布的研究已成为近年来保险精算界一个越来越热门的话题。本文研究了在常数利息力的情况下，索赔额服从重尾分布时，两类延迟更新风险模型的破产概率问题。 本文共四章。 第一章主要介绍本文的研究背景和主要工作内容。 第二章首先简单的介绍了经典Poisson风险模型及其破产概率，然后介绍了重尾分布的概念、包括几类重要的重尾分布子族及其这几类子族之间的关系。 第三章我们用负相依的索赔额来代替独立的索赔额，并且在延迟更新风险模型下，我们得到了索赔额服从ERV族时的最终破产概率的一致渐进表达式： 第四章我们讨论了一个新的风险模型，即延迟复合更新模型。它假设保险公司在同一时刻不止有一位顾客需要索赔，，显然这个模型更符合实际。在这个模型下，我们得到了索赔额服从次指数分布时的破产概率的一致渐进表达式：
[Abstract]:The core problem of risk theory research is the bankruptcy probability of insurance companies, because the heavy-tailed distribution can be used to depict the extreme events in the financial and insurance industry. Therefore, the research on the distribution of claim amount from heavy tail has become a hot topic in the field of actuarial insurance in recent years. In this paper, we study the ruin probability of two kinds of delayed renewal risk models when the claim amount is distributed from heavy tail under the condition of constant interest force. There are four chapters in this paper. The first chapter mainly introduces the research background and main work content of this paper. In the second chapter, we introduce the classical Poisson risk model and its ruin probability, and then introduce the concept of heavy-tailed distribution, including several important heavy-tailed distribution subfamilies and their relations. In Chapter 3, we replace the independent claim amount with negative dependent claim amount, and under the delayed update risk model, We obtain the uniformly asymptotic expression of the final ruin probability of the claim amount from the ERV family. In Chapter 4 we discuss a new risk model, that is, the delayed composite update model. It assumes that insurance companies need more than one customer to claim at the same time, a model that is clearly more realistic. Under this model, we obtain the uniformly progressive expression of ruin probability for the subexponential distribution of the claim amount.
【学位授予单位】：暨南大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;F224;O211.67
本文编号：2255763
[Abstract]:The core problem of risk theory research is the bankruptcy probability of insurance companies, because the heavy-tailed distribution can be used to depict the extreme events in the financial and insurance industry. Therefore, the research on the distribution of claim amount from heavy tail has become a hot topic in the field of actuarial insurance in recent years. In this paper, we study the ruin probability of two kinds of delayed renewal risk models when the claim amount is distributed from heavy tail under the condition of constant interest force. There are four chapters in this paper. The first chapter mainly introduces the research background and main work content of this paper. In the second chapter, we introduce the classical Poisson risk model and its ruin probability, and then introduce the concept of heavy-tailed distribution, including several important heavy-tailed distribution subfamilies and their relations. In Chapter 3, we replace the independent claim amount with negative dependent claim amount, and under the delayed update risk model, We obtain the uniformly asymptotic expression of the final ruin probability of the claim amount from the ERV family. In Chapter 4 we discuss a new risk model, that is, the delayed composite update model. It assumes that insurance companies need more than one customer to claim at the same time, a model that is clearly more realistic. Under this model, we obtain the uniformly progressive expression of ruin probability for the subexponential distribution of the claim amount.
【学位授予单位】：暨南大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;F224;O211.67
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