两类更新风险模型的破产研究
发布时间：2018-10-22 11:45
【摘要】：本文主要研究在两种更新风险模型下的破产概率问题，在更新风险模型下，考虑带风险投资的有限时间破产概率，在复合更新风险模型下，，考虑随机变量和的精细大偏差概率。证明过程采用了Ito’s引理、全期望、Fubini定理、Lebesgue控制收敛定理、Markov不等式以及随机过程等数学工具。全文共分为三章，主要内容为： 第一章为绪论，简单介绍了风险理论以及破产理论的研究情况和发展现状、着重论述了本文的研究背景和意义、重尾分布、风险模型和主要研究内容。 第二章为更新风险模型部分，此章考虑保险公司拿出部分盈余投资Black-Scholes型资本市场指数，在索赔额分布属于L⌒D族的场合下，得到有限时间破产概率的一致渐近表达式。 第三章为复合更新风险模型部分，此章将一般的重尾随机和的精细大偏差尾等价关系式推广到一致变化族上。 总结与展望部分是对全文的总结以及对未来研究提出的建议。
[Abstract]:In this paper, we mainly study the ruin probability under two kinds of renewal risk models. Under the updated risk model, we consider the finite time ruin probability with venture capital, and consider the fine large deviation probability of the sum of random variables in the compound renewal risk model. Ito's Lemma, total expectation, Fubini theorem, Lebesgue control convergence theorem, Markov inequality and stochastic process are used to prove the process. The thesis is divided into three chapters: the first chapter is the introduction, which briefly introduces the risk theory and bankruptcy theory research situation and development status, focusing on the research background and significance of this paper, heavy-tailed distribution, Risk model and main research contents. In the second chapter, the risk model is updated. In this chapter, the uniformly asymptotic expression of the ruin probability of finite time is obtained under the condition that the insurance company takes part of the Black-Scholes capital market index with partial surplus investment and the distribution of the claim amount belongs to the L D family. The third chapter is the risk model of compound renewal. In this chapter, we extend the exact large deviation equivalent relation of the sum of heavy trailing machines to the family of consistent variations. The summary and prospect part is a summary of the full text and suggestions for future research.
【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
本文编号：2287065
[Abstract]:In this paper, we mainly study the ruin probability under two kinds of renewal risk models. Under the updated risk model, we consider the finite time ruin probability with venture capital, and consider the fine large deviation probability of the sum of random variables in the compound renewal risk model. Ito's Lemma, total expectation, Fubini theorem, Lebesgue control convergence theorem, Markov inequality and stochastic process are used to prove the process. The thesis is divided into three chapters: the first chapter is the introduction, which briefly introduces the risk theory and bankruptcy theory research situation and development status, focusing on the research background and significance of this paper, heavy-tailed distribution, Risk model and main research contents. In the second chapter, the risk model is updated. In this chapter, the uniformly asymptotic expression of the ruin probability of finite time is obtained under the condition that the insurance company takes part of the Black-Scholes capital market index with partial surplus investment and the distribution of the claim amount belongs to the L D family. The third chapter is the risk model of compound renewal. In this chapter, we extend the exact large deviation equivalent relation of the sum of heavy trailing machines to the family of consistent variations. The summary and prospect part is a summary of the full text and suggestions for future research.
【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
【参考文献】
相关期刊论文 前1条
1 陈昱;苏淳;;有利息力情形下的有限时间破产概率[J];中国科学技术大学学报;2006年09期
本文编号：2287065
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