重尾相依风险模型的精细大偏差

发布时间：2018-06-03 14:03

  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】：本文要研究的是重尾相依条件下风险模型的大偏差问题.众所周知,在金融保险业中,目前更重视的对象是极端事件.因为这些重大事件不经常发生,可是一旦发生,将会带来巨大损失,导致大索赔额的发生,从而给保险业务带来重大风险.在保险风险理论中,各种破产理论的渐进性的研究与极限理论的大偏差有着密切的关系,故大偏差理论的研究就成为保险公司和广大学者共同关注的重要问题之一.大偏差理论的研究起源于20世纪30年代,一直是概率极限理论领域生机勃勃的分支之一.它对于刻画极端事件具有关键的作用.经过众多学者的研究,已形成了一系列富有特色的研究成果.本文的研究重点是作为承载风险的索赔过程,它们之间不必是独立的,如可以是负相依关系或者其他的相依关系,相应地,索赔间隔时间过程也可以不相互独立.而每个索赔额到来的时候,对保险公司造成的净损失的分布是重尾的.在这些条件下,我们得到的研究结果不仅丰富了保险风险理论,而且也是对大偏差理论及应用的有价值探索. 论文的主要内容分为四章.第一章引言,介绍重尾分布族和相依的有关知识. 第二章介绍重尾分布大偏差的理论.其中包含两方面的知识.第一方面对大偏差理论进行了粗略的概述.大偏差理论分为经典大偏差和精细大偏差.首先给出经典大偏差和精细大偏差的简介,其次从两者对研究对象的要求条件,研究的量,研究结果的表示以及研究的精细程度作出简单对比.最后对精细大偏差的主要研究成果进行论述.第二方面详细介绍了延迟索赔风险模型,该模型有主索赔和由它引起的附索赔两类索赔.因保险公司常常会遇到延迟索赔的情况.例如当一起车祸发生时,担保人不仅要赔付车的损失,而且,如果投保人购买了第三方责任险,担保人还要在随机延迟的一段时间后为第三方进行赔付.在地震、飓风等巨灾风险中通常会有很多风险发生,有些直接可以处理,但有些就需要一定的时间周期才能解决,并且有些风险的发生也会延迟(如地震过后会引发很多疾病的发生,而这些疾病发生的时间都是随机的).由于该模型的现实性,也因此吸引了保险公司和广大学者的关注. 第三章是本论文的主要结果,在延迟索赔风险模型下,突破已有的在轻尾条件下的结果,将其推广到重尾分布和相依随机变量序列,并得到相应的精细大偏差结果.更进一步,在重尾L∩D族下,将索赔额序列是扩展负相依不同分布的条件首次应用到延迟索赔风险模型,而且证得损失过程的部分和与随机和的精细大偏差.该结论不仅推广了单一险种风险模型的已有结论,而且更进一步丰富了现有文献中对延迟索赔风险模型的研究成果. 第四章是对全文的总结及对未来研究内容的展望.
[Abstract]:In this paper, we study the problem of large deviation of risk model under the condition of heavy tail dependence. As we all know, in the financial and insurance industry, the current object of more attention is extreme events. Because these important events do not occur often, but once they occur, it will bring huge losses, leading to the occurrence of large claims, which will bring significant risks to the insurance business. In the insurance risk theory, the gradual research of various bankruptcy theories is closely related to the big deviation of the limit theory, so the research of the big deviation theory has become one of the important problems that the insurance company and the general scholars pay attention to together. The study of large deviation theory, which originated in the 1930s, has been one of the dynamic branches in the field of probability limit theory. It plays a key role in portraying extreme events. Through the research of many scholars, has formed a series of characteristic research results. The emphasis of this paper is that as a claim process bearing risk, it is not necessary for them to be independent, for example, they may be negative dependent or other dependent relationships. Accordingly, the claim interval process may not be independent of each other. When each claim arrives, the distribution of net losses to insurance companies is heavy. Under these conditions, our research results not only enrich the insurance risk theory, but also a valuable exploration for the large deviation theory and its application. The main content of the paper is divided into four chapters. The first chapter introduces the knowledge of heavy-tailed distribution family and dependent family. The second chapter introduces the theory of large deviation of heavy tail distribution. It contains two aspects of knowledge. The first aspect gives a rough overview of the large deviation theory. The theory of large deviation is divided into classical large deviation and fine large deviation. This paper first gives a brief introduction of classical large deviation and fine large deviation, and then makes a simple comparison from the requirements of the two to the object of study, the quantity of the study, the expression of the research results and the degree of fineness of the study. Finally, the main research results of fine large deviation are discussed. In the second part, the risk model of delay claim is introduced in detail. The model has two kinds of claims: master claim and subsidiary claim. Insurance companies often encounter late claims. For example, when a car accident occurs, the guarantor not only has to compensate for the loss of the car, but also, if the policy holder has purchased third-party liability insurance, the guarantor has to pay compensation for the third party after a period of random delay. In earthquakes, hurricanes and other catastrophic risks, there are usually a lot of risks, some can be dealt with directly, but some need a certain period of time to solve the problem. And some risks can be delayed (for example, after an earthquake, many diseases occur at random times. Because of the reality of the model, it attracts the attention of insurance companies and scholars. The third chapter is the main result of this paper. Under the delay claim risk model, we break through the existing results under the condition of light tail, extend it to the heavy tail distribution and dependent random variable sequence, and obtain the corresponding fine large deviation results. Furthermore, under the heavy-tailed L 鈮，

本文编号：1973053