【摘要】：經(jīng)典的二項(xiàng)風(fēng)險(xiǎn)模型是精算文獻(xiàn)中研究得最深入的離散時(shí)間更新風(fēng)險(xiǎn)過(guò)程,近些年來(lái),許多精算學(xué)者從不同的方面把經(jīng)典二項(xiàng)風(fēng)險(xiǎn)模型進(jìn)行了推廣,得到了許多有價(jià)值的結(jié)論.在經(jīng)典的復(fù)合二項(xiàng)風(fēng)險(xiǎn)模型的基礎(chǔ)上,本文研究幾類(lèi)廣義復(fù)合二項(xiàng)風(fēng)險(xiǎn)模型,并且對(duì)這些模型的破產(chǎn)概率做了深入研究. 本論文共分為五章： 第一章本章首先對(duì)風(fēng)險(xiǎn)理論及其核心內(nèi)容破產(chǎn)理論作簡(jiǎn)要介紹,然后對(duì)經(jīng)典復(fù)合二項(xiàng)風(fēng)險(xiǎn)模型做了綜合性的回顧,最后介紹了本文的主要工作. 第二章本章研究具有一般保費(fèi)率的CCBM的破產(chǎn)概率,即索賠次數(shù)過(guò)程為一個(gè)復(fù)合二項(xiàng)過(guò)程,而保費(fèi)率為一個(gè)非負(fù)整數(shù).我們得到了該模型下最終破產(chǎn)概率的表達(dá)式和相應(yīng)的上界估計(jì). 第三章本章研究保費(fèi)收入為復(fù)合二項(xiàng)過(guò)程的CCBM的破產(chǎn)概率,即假設(shè)保費(fèi)收取次數(shù)服從復(fù)合二項(xiàng)分布,而索賠次數(shù)過(guò)程為一個(gè)復(fù)合復(fù)合二項(xiàng)過(guò)程,保費(fèi)率為1,用鞅方法研究該模型下最終破產(chǎn)概率的表達(dá)式和相應(yīng)的上界估計(jì). 第四章本章研究保費(fèi)收入為復(fù)合二項(xiàng)過(guò)程的帶擾動(dòng)CCBM的破產(chǎn)概率,在前一章的基礎(chǔ)上考慮投資與干擾的因素,假設(shè)保費(fèi)收取次數(shù)服從復(fù)合二項(xiàng)分布,而索賠次數(shù)過(guò)程為一個(gè)復(fù)合復(fù)合二項(xiàng)過(guò)程,建立一種貼近現(xiàn)實(shí)的新模型,得到最終破產(chǎn)概率的表達(dá)式和相應(yīng)的上界估計(jì). 第五章本章研究保費(fèi)收入為復(fù)合二項(xiàng)過(guò)程的帶投資和擾動(dòng)CCBM的破產(chǎn)概率,在上一章模型的基礎(chǔ)上考慮到投資利率和通貨膨脹等一些干擾因素對(duì)保險(xiǎn)公司經(jīng)營(yíng)狀態(tài)影響,用鞅方法研究該模型下最終破產(chǎn)概率的表達(dá)式和相應(yīng)的上界估計(jì).
[Abstract]:The classical binomial risk model is the most deeply studied discrete time renewal risk process in the actuarial literature. In recent years, many actuarial scholars have extended the classical binomial risk model from different aspects and obtained many valuable conclusions. On the basis of classical compound binomial risk models, several generalized compound binomial risk models are studied in this paper, and the ruin probability of these models is studied deeply. This paper is divided into five chapters: the first chapter briefly introduces the risk theory and its core theory of bankruptcy, then makes a comprehensive review of the classical compound binomial risk model, and finally introduces the main work of this paper. In chapter 2, we study the ruin probability of CCBM with general premium rate, that is, the process of claim number is a compound binomial process, and the premium rate is a non-negative integer. We obtain the expression of the final ruin probability and the corresponding upper bound estimate. In Chapter 3, we study the ruin probability of CCBM, where the premium income is a compound binomial process, that is, assuming that the premium collection times are distributed from the compound binomial, and the claim number process is a compound binomial process. The premium rate is 1. The expression of the final ruin probability and the corresponding upper bound estimate are studied by martingale method. In chapter 4, we study the ruin probability of perturbed CCBM with a compound binomial process. On the basis of the previous chapter, we consider the factors of investment and disturbance, and assume that the premium collection times are distributed by compound binomial. The process of claim number is a compound binomial process. A new model close to reality is established, and the expression of the final ruin probability and the corresponding upper bound estimate are obtained. In chapter 5, we study the ruin probability with investment and perturbed CCBM when the premium income is a compound binomial process. On the basis of the model in the previous chapter, we consider the influence of some factors such as investment interest rate and inflation on the operating state of the insurance company. The expression of final ruin probability and the corresponding upper bound estimate are studied by martingale method.
【學(xué)位授予單位】：遼寧師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類(lèi)號(hào)】：F840.4;F224

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本文編號(hào)：2208289