重尾索赔风险模型的破产概率及数值模拟
发布时间：2018-09-08 11:18
【摘要】：本文主要研究的是重尾索赔风险模型的破产概率及相应的数值模拟.在金融保险业中,对巨灾产生的大额索赔事件的研究一直是一个热点,这些极端事件不经常发生,一旦发生,将会给保险业务带来重大风险,可能会让保险公司陷入财务危机,甚至破产.近年来,众多学者已经对这些现象进行了大量研究,其中对保险公司破产概率渐近估计的研究更是备受青睐.在众多专家学者的努力下,得到了满足各种不同条件的渐近表达式,但这些研究成果大部分是理论结果,缺乏实践意义.近几年,众多国内外学者已经不满足将研究停留在理论结果上,而是趋向于验证理论结果是否合理,并取得了不错的进展.本文在已有研究成果的基础上有了理论突破,更进一步做了matlab模拟,验证了理论知识的合理性. 此外,本文在考虑重尾现象的同时,还考虑风险索赔之间的相依性.近几年,对保险风险理论的研究多集中在相依情况下.本文也将理论结果扩展到了相依的情况,即上尾相依的特殊情形 上尾独立,使之更贴近实际. 本文主要由三部分组成. 第一章主要介绍了经典风险模型及其推广形式,画出了各种情况下盈余过程的样本轨道图,并进行了比较. 第二章主要内容为潜在索赔风险模型在重尾分布条件下的破产概率和数值模拟.在潜在索赔额序列服从S族的假设下,得到了有限时间破产概率的渐近表达式,并给出了模拟结果. 第三章是对上尾独立情形下潜在索赔风险模型有限时间破产概率的研究,假设索赔额序列是上尾独立同分布的重尾随机变量序列,潜在索赔额序列服从L∩D族,得到了有限时间破产概率的渐近表达式.
[Abstract]:In this paper, the ruin probability of heavy tail claim risk model and its corresponding numerical simulation are studied. In the financial and insurance industry, the study of large claims caused by catastrophe has always been a hot spot. These extreme events do not occur frequently. Once they occur, they will bring significant risks to the insurance business and may lead to financial crisis for insurance companies. Even bankruptcy. In recent years, many scholars have done a lot of research on these phenomena, among which, the research on the asymptotic estimation of bankruptcy probability of insurance companies is more and more popular. Through the efforts of many experts and scholars, the asymptotic expressions satisfying various conditions are obtained, but most of these research results are theoretical results and lack of practical significance. In recent years, many scholars at home and abroad have not satisfied to stay on the theoretical results, but tend to verify whether the theoretical results are reasonable, and have made good progress. In this paper, based on the existing research results, a theoretical breakthrough has been made, and further matlab simulation has been done to verify the rationality of the theoretical knowledge. In addition, we consider the dependence of risk claims as well as the heavy-tailed phenomenon. In recent years, the study of insurance risk theory is mostly focused on dependent cases. In this paper, the theoretical results are extended to the dependent case, that is, the special case of the dependency of the upper tail and the tail is independent, so that it is closer to the reality. This paper mainly consists of three parts. The first chapter mainly introduces the classical risk model and its extension form, draws the sample track diagram of the surplus process under various circumstances, and compares it with each other. The second chapter focuses on the ruin probability and numerical simulation of the potential claim risk model under the condition of heavy-tailed distribution. Under the assumption of S family, the asymptotic expression of ruin probability in finite time is obtained, and the simulation results are given. In the third chapter, we study the finite time ruin probability of the potential claim risk model in the case of upper tail independence, assuming that the claim amount sequence is a sequence of heavy-tailed random variables with the same distribution of upper tail independence, and the potential claim amount sequence is followed by L 鈮，
本文编号：2230369
[Abstract]:In this paper, the ruin probability of heavy tail claim risk model and its corresponding numerical simulation are studied. In the financial and insurance industry, the study of large claims caused by catastrophe has always been a hot spot. These extreme events do not occur frequently. Once they occur, they will bring significant risks to the insurance business and may lead to financial crisis for insurance companies. Even bankruptcy. In recent years, many scholars have done a lot of research on these phenomena, among which, the research on the asymptotic estimation of bankruptcy probability of insurance companies is more and more popular. Through the efforts of many experts and scholars, the asymptotic expressions satisfying various conditions are obtained, but most of these research results are theoretical results and lack of practical significance. In recent years, many scholars at home and abroad have not satisfied to stay on the theoretical results, but tend to verify whether the theoretical results are reasonable, and have made good progress. In this paper, based on the existing research results, a theoretical breakthrough has been made, and further matlab simulation has been done to verify the rationality of the theoretical knowledge. In addition, we consider the dependence of risk claims as well as the heavy-tailed phenomenon. In recent years, the study of insurance risk theory is mostly focused on dependent cases. In this paper, the theoretical results are extended to the dependent case, that is, the special case of the dependency of the upper tail and the tail is independent, so that it is closer to the reality. This paper mainly consists of three parts. The first chapter mainly introduces the classical risk model and its extension form, draws the sample track diagram of the surplus process under various circumstances, and compares it with each other. The second chapter focuses on the ruin probability and numerical simulation of the potential claim risk model under the condition of heavy-tailed distribution. Under the assumption of S family, the asymptotic expression of ruin probability in finite time is obtained, and the simulation results are given. In the third chapter, we study the finite time ruin probability of the potential claim risk model in the case of upper tail independence, assuming that the claim amount sequence is a sequence of heavy-tailed random variables with the same distribution of upper tail independence, and the potential claim amount sequence is followed by L 鈮，
本文编号：2230369
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