發(fā)布時間：2019-05-07 16:59

【摘要】：近年來,風險理論發(fā)展十分迅速,眾多學者致力于保險公司破產(chǎn)概率的研究,涌現(xiàn)出很多新的風險模型,豐富和完善了風險理論；大部分學者對破產(chǎn)概率的研究主要集中于對破產(chǎn)時間、破產(chǎn)前瞬間盈余、破產(chǎn)時刻赤字等變量的研究,很少有學者對破產(chǎn)索賠次數(shù)與破產(chǎn)時間之間的關(guān)系進行研究；因此,將索賠次數(shù)和破產(chǎn)時間放在一起研究是一個比較新的,有意義的課題,一些關(guān)于破產(chǎn)時間的已知結(jié)果可以用破產(chǎn)時的索賠次數(shù)來解釋；研究不同風險模型下第n次索賠的破產(chǎn)概率具有一定的理論價值和現(xiàn)實指導意義,是一個非常有意義的課題。 本文首先介紹了風險理論的一些基本的知識和方法；然后為了使風險模型更符合實際情況,在經(jīng)典風險模型的基礎(chǔ)上,研究了風險事件不等同于索賠事件的Poisson-Geometric風險模型；通過構(gòu)造一類Gerber-Shiu函數(shù),分別推導出該風險模型下Gerber-Shiu函數(shù)滿足的更新方程,破產(chǎn)時刻和直到破產(chǎn)時的索賠次數(shù)的聯(lián)合密度函數(shù),最終得到了第n次索賠時的破產(chǎn)概率的數(shù)學表達式。又考慮到經(jīng)典風險模型中,保險公司只面對單風險的情形,但現(xiàn)實生活中,保險公司會承擔不同的保險業(yè)務(wù)；因此,本文又研究了獨立二元風險模型和一類索賠相依的二元風險模型的破產(chǎn)問題,最終得到了這兩種風險模型下第n次索賠時的破產(chǎn)概率的數(shù)學表達式。 最后,對本文的研究結(jié)果作了一個總結(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.
【學位授予單位】：安徽工程大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：F840;F224

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