【摘要】：對(duì)于經(jīng)典風(fēng)險(xiǎn)模型的研究,都是基于保費(fèi)收入是線性增長(zhǎng)和理賠過(guò)程是Poisson的這兩個(gè)重要的假設(shè)條件之下。但是隨著保險(xiǎn)業(yè)的發(fā)展,我們發(fā)現(xiàn)在實(shí)際運(yùn)營(yíng)過(guò)程中,這些條件與保險(xiǎn)公司當(dāng)前的實(shí)際情況越來(lái)越不符合。因此,研究出一個(gè)更為貼近保險(xiǎn)公司實(shí)務(wù)的風(fēng)險(xiǎn)模型成為了當(dāng)代精算學(xué)者們的當(dāng)務(wù)之急。許多精算學(xué)者投入了大量的精力,并取得了豐碩的成果。 本文就是在繼承前人的研究成果之上,綜合考慮對(duì)保費(fèi)收入和對(duì)理賠過(guò)程兩種類(lèi)型的推廣,主要構(gòu)建了兩種非線性的保費(fèi)收入的相依風(fēng)險(xiǎn)模型,使得模型更貼近保險(xiǎn)實(shí)務(wù)。并通過(guò)運(yùn)用復(fù)分析、隨機(jī)過(guò)程以及風(fēng)險(xiǎn)理論等學(xué)科理論知識(shí)來(lái)研究了這兩類(lèi)模型的期望折現(xiàn)罰金函數(shù)的計(jì)算方法。本文的內(nèi)容框架如下： 第一章首先對(duì)經(jīng)典風(fēng)險(xiǎn)模型以及它所具備的特征作了簡(jiǎn)單的介紹；其次,結(jié)合本文的主要研究?jī)?nèi)容,我們簡(jiǎn)要回顧了目前國(guó)內(nèi)外相關(guān)方面的研究現(xiàn)狀；最后介紹本文的主要研究?jī)?nèi)容。 第二章首先給出了若干約定；其次結(jié)合本文理論研究過(guò)程的需要,給出了一些研究過(guò)程中所涉及的相關(guān)知識(shí)以及研究所需的工具方法。 第三章通過(guò)將保費(fèi)收入過(guò)程從經(jīng)典風(fēng)險(xiǎn)模型中的線性增長(zhǎng)推廣到非線性的Poisson過(guò)程,以及考慮到理賠過(guò)程中理賠間隔時(shí)間與理賠額之間實(shí)際中應(yīng)存在著一定的依賴(lài)關(guān)系,構(gòu)建了Poisson保費(fèi)收入的一類(lèi)相依情形下的更新風(fēng)險(xiǎn)模型,其中保費(fèi)收入是Poisson的,且理賠間隔時(shí)間與理賠額之間的依賴(lài)關(guān)系滿(mǎn)足Boudreault et alo.(2006)中所提出的依賴(lài)關(guān)系。此外,本章討論了該模型下的Gerber-Shiu函數(shù)的計(jì)算方法,并成功推導(dǎo)出其生成函數(shù)的精確表達(dá)式,并且得到了生成函數(shù)所滿(mǎn)足的瑕疵更新方程的顯示表達(dá)式。 第四章,我們?cè)诘谌碌难芯炕A(chǔ)之上把保費(fèi)收入過(guò)程進(jìn)一步推廣到復(fù)合Poisson過(guò)程的相依更新風(fēng)險(xiǎn)模型。其所滿(mǎn)足的相依關(guān)系依然是Boudreault et al.(2006)中提出的。本章通過(guò)考慮首次理賠間隔時(shí)間和首次發(fā)生保費(fèi)收入的到達(dá)時(shí)刻之間的關(guān)系,推導(dǎo)出此相依情形下的Gerber-Shiu函數(shù)的Laplace變換的顯示表達(dá)式.
[Abstract]:The study of classical risk model is based on the assumption that premium income is linear growth and claim process is Poisson. However, with the development of insurance industry, we find that these conditions are more and more inconsistent with the actual situation of insurance companies. Therefore, to develop a risk model closer to the practice of insurance companies has become an urgent task for modern actuaries. Many actuaries have invested a great deal of energy and achieved fruitful results. In this paper, based on the previous research results, we consider the generalization of premium income and claim process synthetically, and construct two nonlinear risk models of premium income, which make the model more close to insurance practice. By using the knowledge of complex analysis, stochastic process and risk theory, this paper studies the calculation method of the expected discounted penalty function of these two kinds of models. The main contents of this paper are as follows: the first chapter introduces the classical risk model and its characteristics. Secondly, combined with the main research content of this paper, we briefly review the current research situation at home and abroad, and finally introduce the main research content of this paper. In the second chapter, some conventions are given first, and then some relevant knowledge and tools are given according to the needs of the theoretical research process in this paper. The third chapter extends the premium income process from the linear growth in the classical risk model to the nonlinear Poisson process, and considers that there should be a certain dependence between the claim interval and the amount of claim in the process of settlement. In this paper, an update risk model of Poisson premium income is constructed, in which the premium income is Poisson, and the dependence between claim interval and claim amount satisfies the dependency proposed in Boudreault et alo. (2006). In addition, this chapter discusses the calculation method of the Gerber-Shiu function under the model, and successfully deduces the exact expression of the generating function, and obtains the display expression of the defective update equation satisfied by the generating function. In Chapter 4, we extend the premium income process to the dependent renewal risk model of the compound Poisson process based on the research in Chapter 3. The dependent relation it satisfies is still proposed in Boudreault et al. (2006). In this chapter, by considering the relationship between the interval between the first claim and the arrival time of the first premium income, the expression of the Laplace transform of the Gerber-Shiu function in this dependent case is derived.
【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(lèi)號(hào)】：F840;F224

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本文編號(hào)：2421261