本文選題：重尾分布 + 負(fù)相依��； 參考：《西北師范大學(xué)》2013年碩士論文

【摘要】：本文要研究的是重尾相依條件下風(fēng)險模型的大偏差問題.眾所周知,在金融保險業(yè)中,目前更重視的對象是極端事件.因為這些重大事件不經(jīng)常發(fā)生,可是一旦發(fā)生,將會帶來巨大損失,導(dǎo)致大索賠額的發(fā)生,從而給保險業(yè)務(wù)帶來重大風(fēng)險.在保險風(fēng)險理論中,各種破產(chǎn)理論的漸進(jìn)性的研究與極限理論的大偏差有著密切的關(guān)系,故大偏差理論的研究就成為保險公司和廣大學(xué)者共同關(guān)注的重要問題之一.大偏差理論的研究起源于20世紀(jì)30年代,一直是概率極限理論領(lǐng)域生機勃勃的分支之一.它對于刻畫極端事件具有關(guān)鍵的作用.經(jīng)過眾多學(xué)者的研究,已形成了一系列富有特色的研究成果.本文的研究重點是作為承載風(fēng)險的索賠過程,它們之間不必是獨立的,如可以是負(fù)相依關(guān)系或者其他的相依關(guān)系,相應(yīng)地,索賠間隔時間過程也可以不相互獨立.而每個索賠額到來的時候,對保險公司造成的凈損失的分布是重尾的.在這些條件下,我們得到的研究結(jié)果不僅豐富了保險風(fēng)險理論,而且也是對大偏差理論及應(yīng)用的有價值探索. 論文的主要內(nèi)容分為四章.第一章引言,介紹重尾分布族和相依的有關(guān)知識. 第二章介紹重尾分布大偏差的理論.其中包含兩方面的知識.第一方面對大偏差理論進(jìn)行了粗略的概述.大偏差理論分為經(jīng)典大偏差和精細(xì)大偏差.首先給出經(jīng)典大偏差和精細(xì)大偏差的簡介,其次從兩者對研究對象的要求條件,研究的量,研究結(jié)果的表示以及研究的精細(xì)程度作出簡單對比.最后對精細(xì)大偏差的主要研究成果進(jìn)行論述.第二方面詳細(xì)介紹了延遲索賠風(fēng)險模型,該模型有主索賠和由它引起的附索賠兩類索賠.因保險公司常常會遇到延遲索賠的情況.例如當(dāng)一起車禍發(fā)生時,擔(dān)保人不僅要賠付車的損失,而且,如果投保人購買了第三方責(zé)任險,擔(dān)保人還要在隨機延遲的一段時間后為第三方進(jìn)行賠付.在地震、颶風(fēng)等巨災(zāi)風(fēng)險中通常會有很多風(fēng)險發(fā)生,有些直接可以處理,但有些就需要一定的時間周期才能解決,并且有些風(fēng)險的發(fā)生也會延遲(如地震過后會引發(fā)很多疾病的發(fā)生,而這些疾病發(fā)生的時間都是隨機的).由于該模型的現(xiàn)實性,也因此吸引了保險公司和廣大學(xué)者的關(guān)注. 第三章是本論文的主要結(jié)果,在延遲索賠風(fēng)險模型下,突破已有的在輕尾條件下的結(jié)果,將其推廣到重尾分布和相依隨機變量序列,并得到相應(yīng)的精細(xì)大偏差結(jié)果.更進(jìn)一步,在重尾L∩D族下,將索賠額序列是擴(kuò)展負(fù)相依不同分布的條件首次應(yīng)用到延遲索賠風(fēng)險模型,而且證得損失過程的部分和與隨機和的精細(xì)大偏差.該結(jié)論不僅推廣了單一險種風(fēng)險模型的已有結(jié)論,而且更進(jìn)一步豐富了現(xiàn)有文獻(xiàn)中對延遲索賠風(fēng)險模型的研究成果. 第四章是對全文的總結(jié)及對未來研究內(nèi)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，

本文編號：1973053