本文關(guān)鍵詞： 一致漸近性 布朗運(yùn)動(dòng) 相依 有限時(shí)間破產(chǎn)概率　出處：《曲阜師范大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：本文考慮了兩類帶布朗運(yùn)動(dòng)干擾和常利率的n維更新風(fēng)險(xiǎn)模型有限時(shí)間的破產(chǎn)概率的一致漸近性.其中一類風(fēng)險(xiǎn)模型中的n種索賠來到的時(shí)間是不同的;另一類的n種索賠來到的時(shí)間是相同的.在這兩類n維風(fēng)險(xiǎn)模型中, n種索賠的索賠額的大小是上尾漸近獨(dú)立(英文簡(jiǎn)寫為UTAI,見定義2.4)的隨機(jī)變量,它們的分布函數(shù)同時(shí)屬于長(zhǎng)尾分布類(見定義2.2)和主導(dǎo)變化尾分布類(見定義2.2),而且來到時(shí)間間隔服從廣義下限相依結(jié)構(gòu)(英文簡(jiǎn)寫為WLOD,見定義2.3). 本文所討論的兩類n維更新風(fēng)險(xiǎn)模型，，其中的一類可以表示一個(gè)保險(xiǎn)公司有n種不同的保險(xiǎn)業(yè)務(wù)且這些保險(xiǎn)業(yè)務(wù)的索賠來到時(shí)刻是不相同的;而另外一類可以表示一個(gè)保險(xiǎn)公司的n種不同的保險(xiǎn)業(yè)務(wù)的索賠來到時(shí)刻是相同的.本文的主要目的是研究這兩類風(fēng)險(xiǎn)模型的三種有限時(shí)間的破產(chǎn)概率的一致漸近性.我們定義了三種多維的非標(biāo)準(zhǔn)的更新風(fēng)險(xiǎn)模型的破產(chǎn)時(shí).這三種破產(chǎn)時(shí)分別是:一、保險(xiǎn)公司中的每一個(gè)業(yè)務(wù)的盈余都達(dá)到負(fù)值的最小時(shí)間;二、保險(xiǎn)公司中至少有一個(gè)業(yè)務(wù)的盈余達(dá)到負(fù)值的最小時(shí)間;三、保險(xiǎn)公司中的所有業(yè)務(wù)盈余的和值達(dá)到負(fù)值的最小時(shí)間.對(duì)應(yīng)每一種破產(chǎn)時(shí)我們相應(yīng)的定義了一種破產(chǎn)概率.最后,我們得到了這三種有限時(shí)間破產(chǎn)概率的一致漸近性. 根據(jù)文章的主要內(nèi)容,本文可分為以下五章:第一章描述了本文所要研究的兩類多維風(fēng)險(xiǎn)模型;第二章的預(yù)備知識(shí)主要介紹了本文中所用到的定義和一些背景;在第三章中給出了本文的一些結(jié)果;在第四章中我們給出了一些引理;最后是主要結(jié)果的證明.
[Abstract]:In this paper, we consider the uniform asymptotic behavior of ruin probability for two classes of n-dimensional renewal risk models with Brownian motion disturbance and constant interest rate. In these two types of n-dimensional risk models, the claim amount of n claims is a random variable whose upper tail is asymptotically independent (UTAI, see definition 2.4). Their distribution functions belong to both the long-tailed distribution class (see definition 2.2) and the dominant variable-tail distribution class (see definition 2.2), and come to the interval from the generalized lower bound dependent structure (WLOD). In this paper, two classes of n-dimensional renewal risk models are discussed, one of which can indicate that an insurance company has n different types of insurance business and the claims for these insurance services are different at the time of arrival. The other kind of claim that can represent n different kinds of insurance business of an insurance company is at the same time. The main purpose of this paper is to study the consistency of ruin probability of three kinds of finite time of these two kinds of risk models. Nearness. We define the ruin time of three multidimensional non-standard renewal risk models. The three kinds of ruin time are as follows: 1. The minimum time for each business surplus in an insurance company to be negative; second, for at least one business in an insurance company to reach a negative value; third, The minimum time for the sum of all the business surpluses in insurance companies to be negative. For each ruin we define a ruin probability. Finally we obtain the uniform asymptotic property of the three finite time ruin probabilities. According to the main contents of this paper, this paper can be divided into the following five chapters: the first chapter describes the two kinds of multi-dimensional risk models to be studied in this paper, the second chapter introduces the definitions and some background used in this paper. In the third chapter, we give some results of this paper; in Chapter 4th, we give some lemmas; finally, we prove the main results.
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：O211.6;F840.31

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 ;FINITE-TIME RUIN PROBABILITY WITH NQD DOMINATED VARYING-TAILED CLAIMS AND NLOD INTER-ARRIVAL TIMES[J];Journal of Systems Science & Complexity;2009年03期

本文編號(hào)：1499250