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】：自從上個(gè)世紀(jì)60年代以來(lái),重尾分布在應(yīng)用概率領(lǐng)域,特別是在分支過(guò)程,排隊(duì)論及風(fēng)險(xiǎn)理論等領(lǐng)域有著廣泛的應(yīng)用.在保險(xiǎn)業(yè)中,許多重大的風(fēng)險(xiǎn)都是由一些大額索賠造成的,如火險(xiǎn),風(fēng)暴險(xiǎn)和地震險(xiǎn)等.由于重尾分布能刻畫大額索賠這一特性.因此,人們有必要對(duì)重尾分布發(fā)生的規(guī)律進(jìn)行研究,這對(duì)保險(xiǎn)經(jīng)營(yíng)過(guò)程中的風(fēng)險(xiǎn)評(píng)估與預(yù)測(cè)提供理論工具.同時(shí),在早期的保險(xiǎn)風(fēng)險(xiǎn)中,人們將賠付額以及索賠發(fā)生的間隔時(shí)間均視為獨(dú)立同分布的隨機(jī)變量.然而,在現(xiàn)實(shí)生活中,它們之間存在著某種相依關(guān)系. 本文仍然以重尾分布為主要對(duì)象,討論了相依索賠下風(fēng)險(xiǎn)模型的精細(xì)大偏差及其破產(chǎn)概率的漸近性.在第一章中,本文介紹了相關(guān)的重尾分布,相依的概念以及重尾相依隨機(jī)變量的研究現(xiàn)狀.在第二章中,構(gòu)建了基于客戶到來(lái)風(fēng)險(xiǎn)模型,通過(guò)示性函數(shù)將賠付額精確的表達(dá)出來(lái).在索賠額隨機(jī)變量為負(fù)相依且有共同分布屬于L∩D族下,討論了該風(fēng)險(xiǎn)模型損失過(guò)程的部分和和隨機(jī)和的精細(xì)大偏差.更進(jìn)一步地,得到了該風(fēng)險(xiǎn)模型盈余過(guò)程的有限時(shí)間破產(chǎn)概率的漸近關(guān)系.大偏差概率可以應(yīng)用于大額索賠保險(xiǎn)的情形下,尤其是再保險(xiǎn).值得指出的是,隨機(jī)和精細(xì)大偏差的結(jié)果對(duì)于一些風(fēng)險(xiǎn)預(yù)測(cè)的評(píng)估有非常重要作用.如大型保險(xiǎn)公司投資組合的總索賠風(fēng)險(xiǎn)的條件尾期望和價(jià)值.在風(fēng)險(xiǎn)理論中,研究破產(chǎn)概率可以為保險(xiǎn)公司的決策者提供一個(gè)早期的風(fēng)險(xiǎn)警示,也是衡量一個(gè)保險(xiǎn)公司及其所經(jīng)營(yíng)某個(gè)險(xiǎn)種的金融風(fēng)險(xiǎn)的極其重要的尺度.因此,風(fēng)險(xiǎn)模型破產(chǎn)概率的研究對(duì)保險(xiǎn)公司的經(jīng)營(yíng)有非常重要的指導(dǎo)意義.第三章中,索賠額為負(fù)相依同分布的重尾隨機(jī)變量,引進(jìn)一個(gè)可測(cè)函數(shù),得到索賠額和索賠時(shí)間間隔的相依關(guān)系.假設(shè)索賠額分布為L(zhǎng)∩D族,建立了有限時(shí)間破產(chǎn)概率的弱漸近等價(jià)式.進(jìn)而,得到了連續(xù)時(shí)間的常利息力更新風(fēng)險(xiǎn)模型的結(jié)果.由破產(chǎn)概率的漸近關(guān)系得出有限時(shí)間破產(chǎn)概率對(duì)于索賠額的負(fù)相依結(jié)構(gòu)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，

本文編號(hào)：1931635