相依索赔下风险模型的大偏差及破产概率

发布时间：2018-05-25 02:18

  本文选题：重尾分布 + 负相依　； 参考：《西北师范大学》2013年硕士论文

【摘要】：自从上个世纪60年代以来,重尾分布在应用概率领域,特别是在分支过程,排队论及风险理论等领域有着广泛的应用.在保险业中,许多重大的风险都是由一些大额索赔造成的,如火险,风暴险和地震险等.由于重尾分布能刻画大额索赔这一特性.因此,人们有必要对重尾分布发生的规律进行研究,这对保险经营过程中的风险评估与预测提供理论工具.同时,在早期的保险风险中,人们将赔付额以及索赔发生的间隔时间均视为独立同分布的随机变量.然而,在现实生活中,它们之间存在着某种相依关系. 本文仍然以重尾分布为主要对象,讨论了相依索赔下风险模型的精细大偏差及其破产概率的渐近性.在第一章中,本文介绍了相关的重尾分布,相依的概念以及重尾相依随机变量的研究现状.在第二章中,构建了基于客户到来风险模型,通过示性函数将赔付额精确的表达出来.在索赔额随机变量为负相依且有共同分布属于L∩D族下,讨论了该风险模型损失过程的部分和和随机和的精细大偏差.更进一步地,得到了该风险模型盈余过程的有限时间破产概率的渐近关系.大偏差概率可以应用于大额索赔保险的情形下,尤其是再保险.值得指出的是,随机和精细大偏差的结果对于一些风险预测的评估有非常重要作用.如大型保险公司投资组合的总索赔风险的条件尾期望和价值.在风险理论中,研究破产概率可以为保险公司的决策者提供一个早期的风险警示,也是衡量一个保险公司及其所经营某个险种的金融风险的极其重要的尺度.因此,风险模型破产概率的研究对保险公司的经营有非常重要的指导意义.第三章中,索赔额为负相依同分布的重尾随机变量,引进一个可测函数,得到索赔额和索赔时间间隔的相依关系.假设索赔额分布为L∩D族,建立了有限时间破产概率的弱渐近等价式.进而,得到了连续时间的常利息力更新风险模型的结果.由破产概率的渐近关系得出有限时间破产概率对于索赔额的负相依结构是不敏感的.
[Abstract]:Since the 1960s, the heavy-tailed distribution has been widely used in the fields of applied probability, especially in branching process, queuing and risk theory. In the insurance industry, many major risks are caused by large claims, such as fire, storm and earthquake risks. Because the heavy-tailed distribution can describe the characteristics of large claims. Therefore, it is necessary to study the occurrence of heavy-tailed distribution, which provides a theoretical tool for risk assessment and prediction in the process of insurance management. At the same time, in the early insurance risk, the amount of compensation and the interval between claims are regarded as independent and distributed random variables. However, in real life, there is a certain relationship between them. In this paper, we still take the heavy-tailed distribution as the main object, and discuss the fine large deviation of risk model and the asymptotic property of ruin probability under the dependent claim. In the first chapter, we introduce the concepts of heavy-tailed distribution, dependency and the research status of heavy-tailed random variables. In the second chapter, the customer arrival risk model is constructed, and the exact expression of the compensation amount is obtained by means of the indicative function. Under the condition that the random variables of the claim amount are negative dependent and have a common distribution, the fine large deviations of the partial sum and the random sum of the loss process of the risk model are discussed. Furthermore, the asymptotic relation of the finite time ruin probability of the risk model surplus process is obtained. Large deviation probability can be applied to large claim insurance, especially reinsurance. It is worth noting that the results of random and fine large deviations are very important for the assessment of some risk forecasts. Such as large insurance company portfolio of total claim risk conditions end expectation and value. In the risk theory, the study of bankruptcy probability can provide an early risk warning for the policy makers of insurance companies, and it is also an extremely important measure to measure the financial risk of an insurance company and its type of insurance. Therefore, the study of the ruin probability of risk model has a very important guiding significance for the management of insurance companies. In chapter 3, the claim amount is a negative dependent distribution of heavy-tailed random variable. A measurable function is introduced to obtain the dependence between the claim amount and the claim time interval. The weakly asymptotically equivalent formula for the ruin probability of finite time is established, assuming that the claim amount is distributed as L 鈮，

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