【摘要】：近年來(lái),風(fēng)險(xiǎn)理論發(fā)展十分迅速,眾多學(xué)者致力于保險(xiǎn)公司破產(chǎn)概率的研究,涌現(xiàn)出很多新的風(fēng)險(xiǎn)模型,豐富和完善了風(fēng)險(xiǎn)理論；大部分學(xué)者對(duì)破產(chǎn)概率的研究主要集中于對(duì)破產(chǎn)時(shí)間、破產(chǎn)前瞬間盈余、破產(chǎn)時(shí)刻赤字等變量的研究,很少有學(xué)者對(duì)破產(chǎn)索賠次數(shù)與破產(chǎn)時(shí)間之間的關(guān)系進(jìn)行研究；因此,將索賠次數(shù)和破產(chǎn)時(shí)間放在一起研究是一個(gè)比較新的,有意義的課題,一些關(guān)于破產(chǎn)時(shí)間的已知結(jié)果可以用破產(chǎn)時(shí)的索賠次數(shù)來(lái)解釋；研究不同風(fēng)險(xiǎn)模型下第n次索賠的破產(chǎn)概率具有一定的理論價(jià)值和現(xiàn)實(shí)指導(dǎo)意義,是一個(gè)非常有意義的課題。 本文首先介紹了風(fēng)險(xiǎn)理論的一些基本的知識(shí)和方法；然后為了使風(fēng)險(xiǎn)模型更符合實(shí)際情況,在經(jīng)典風(fēng)險(xiǎn)模型的基礎(chǔ)上,研究了風(fēng)險(xiǎn)事件不等同于索賠事件的Poisson-Geometric風(fēng)險(xiǎn)模型；通過(guò)構(gòu)造一類Gerber-Shiu函數(shù),分別推導(dǎo)出該風(fēng)險(xiǎn)模型下Gerber-Shiu函數(shù)滿足的更新方程,破產(chǎn)時(shí)刻和直到破產(chǎn)時(shí)的索賠次數(shù)的聯(lián)合密度函數(shù),最終得到了第n次索賠時(shí)的破產(chǎn)概率的數(shù)學(xué)表達(dá)式。又考慮到經(jīng)典風(fēng)險(xiǎn)模型中,保險(xiǎn)公司只面對(duì)單風(fēng)險(xiǎn)的情形,但現(xiàn)實(shí)生活中,保險(xiǎn)公司會(huì)承擔(dān)不同的保險(xiǎn)業(yè)務(wù)；因此,本文又研究了獨(dú)立二元風(fēng)險(xiǎn)模型和一類索賠相依的二元風(fēng)險(xiǎn)模型的破產(chǎn)問(wèn)題,最終得到了這兩種風(fēng)險(xiǎn)模型下第n次索賠時(shí)的破產(chǎn)概率的數(shù)學(xué)表達(dá)式。 最后,對(duì)本文的研究結(jié)果作了一個(gè)總結(jié),給出了本文的展望。
[Abstract]:In recent years, the risk theory develops very rapidly, many scholars devote to the insurance company bankruptcy probability research, emerged many new risk models, enriched and perfected the risk theory; The majority of scholars mainly focus on the bankruptcy time, the instant surplus before bankruptcy, the deficit at the ruin time and so on. Few scholars study the relationship between the number of bankruptcy claims and the bankruptcy time, and few scholars study the relationship between the number of bankruptcy claims and the bankruptcy time. Therefore, the study of the number of claims and the time of bankruptcy together is a relatively new and meaningful subject, and some known results about the time of bankruptcy can be explained by the number of claims at the time of bankruptcy; The research on the ruin probability of the nth claim under different risk models has certain theoretical value and practical guiding significance, and it is a very meaningful subject. This paper first introduces some basic knowledge and methods of risk theory, and then, in order to make the risk model more suitable to the actual situation, on the basis of the classical risk model, studies the Poisson-Geometric risk model of risk event which is not equal to the claim event; By constructing a class of Gerber-Shiu function, the renewal equation of Gerber-Shiu function under the risk model, the joint density function of the time of ruin and the number of claims until ruin are derived, respectively. Finally, the mathematical expression of the ruin probability of the nth claim is obtained. Taking into account the classical risk model, insurance companies only face the case of single risk, but in real life, insurance companies will assume different insurance business; Therefore, the ruin problem of independent dualistic risk model and a kind of dependent dualistic risk model is studied in this paper. Finally, the mathematical expression of the ruin probability of the nth claim under these two risk models is obtained. Finally, the research results of this paper are summarized, and the prospect of this paper is given.
【學(xué)位授予單位】：安徽工程大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F840;F224

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