本文選題：保險(xiǎn)風(fēng)險(xiǎn)和金融風(fēng)險(xiǎn) + 廣義FGM分布　； 參考：《重慶理工大學(xué)》2017年碩士論文

【摘要】：近年來(lái),風(fēng)險(xiǎn)理論一直是精算數(shù)學(xué)和應(yīng)用概率研究的熱門課題之一,其核心問(wèn)題就是研究破產(chǎn)理論。因?yàn)槠飘a(chǎn)理論在風(fēng)險(xiǎn)管理中具有廣泛的應(yīng)用價(jià)值,從而受到了國(guó)內(nèi)外學(xué)者們廣泛關(guān)注。隨著破產(chǎn)理論的研究深入,在研究的時(shí)候我們需要考慮的因素也就越來(lái)越多,比如隨機(jī)經(jīng)濟(jì)環(huán)境中的隨機(jī)利率,隨機(jī)投資回報(bào)率等,并且這些因素之間還存在相依關(guān)系。實(shí)際上,隨著經(jīng)濟(jì)的發(fā)展,保險(xiǎn)公司為了獲得更多的收益,會(huì)將自己的部分資產(chǎn)作投資,從而,保險(xiǎn)公司在隨機(jī)經(jīng)濟(jì)環(huán)境中將要面臨兩種風(fēng)險(xiǎn),一種是傳統(tǒng)的理賠責(zé)任險(xiǎn)保單組合,另一種是風(fēng)險(xiǎn)投資導(dǎo)致投資風(fēng)險(xiǎn)。顯然,這兩種風(fēng)險(xiǎn)并不獨(dú)立的,而是,金融風(fēng)險(xiǎn)對(duì)保險(xiǎn)公司的影響越來(lái)越嚴(yán)重。因此,研究帶有保險(xiǎn)風(fēng)險(xiǎn)與金融風(fēng)險(xiǎn)的相依風(fēng)險(xiǎn)模型更具有現(xiàn)實(shí)意義。在過(guò)去大量的文獻(xiàn)利用隨機(jī)過(guò)程、乘積理論、重尾分布理論等致力于研究保險(xiǎn)風(fēng)險(xiǎn)與金融風(fēng)險(xiǎn)相互獨(dú)立的情形時(shí)的破產(chǎn)概率漸近等價(jià)式。本文利用隨機(jī)變量乘積理論、重尾分布理論等討論離散時(shí)間的保險(xiǎn)風(fēng)險(xiǎn)與金融風(fēng)險(xiǎn)相依問(wèn)題,主要研究?jī)?nèi)容如下:首先,研究了相依隨機(jī)變量乘積的尾概率問(wèn)題,它們是后文研究的數(shù)學(xué)理論基礎(chǔ)。接著,我們將推導(dǎo)的結(jié)論應(yīng)用到保險(xiǎn)風(fēng)險(xiǎn)研究中,我們考慮保險(xiǎn)風(fēng)險(xiǎn)與金融風(fēng)險(xiǎn)構(gòu)成的獨(dú)立同分布隨機(jī)向量序列服從廣義FGM分布,保險(xiǎn)風(fēng)險(xiǎn)屬于(?)族,在一些特殊的條件下推得了一些精確的有限時(shí)間的破產(chǎn)概率漸近等價(jià)式和無(wú)限時(shí)間的破產(chǎn)概率漸近等價(jià)式。在上述研究中,推導(dǎo)的部分破產(chǎn)概率的漸近等價(jià)式具有線性組合的形式,該線性組合是由保險(xiǎn)風(fēng)險(xiǎn)與金融風(fēng)險(xiǎn)尾概率構(gòu)成。這樣的等價(jià)式更能體現(xiàn)出金融風(fēng)險(xiǎn)對(duì)保險(xiǎn)公司的影響。豐富和發(fā)展了保險(xiǎn)風(fēng)險(xiǎn)與金融風(fēng)險(xiǎn)相依理論。
[Abstract]:In recent years, risk theory has been one of the hot topics in actuarial mathematics and applied probability research, and its core problem is to study bankruptcy theory. Because bankruptcy theory has wide application value in risk management, scholars at home and abroad pay close attention to it. With the further study of bankruptcy theory, there are more and more factors we need to consider, such as the stochastic interest rate in the stochastic economic environment, the rate of return on stochastic investment and so on, and these factors are still dependent on each other. In fact, with the development of the economy, insurance companies will invest some of their assets in order to get more income, so the insurance companies will face two kinds of risks in the random economic environment. One is the traditional claim liability insurance policy portfolio, the other is the investment risk caused by venture capital. Obviously, these two kinds of risk are not independent, but the financial risk to the insurance company's influence is increasingly serious. Therefore, it is of practical significance to study the dependent risk model with insurance risk and financial risk. In the past, a large number of literatures have been devoted to studying the asymptotic equivalent of ruin probability when insurance risk and financial risk are independent of each other by means of stochastic process, product theory and heavy-tailed distribution theory. In this paper, the dependence of discrete time insurance risk and financial risk is discussed by means of random variable product theory and heavy-tailed distribution theory. The main research contents are as follows: firstly, the end probability problem of the product of dependent random variable is studied. They are the mathematical theory foundation of the later study. Then, we apply the conclusion to the study of insurance risk. We consider the independent same distribution random vector sequence of insurance risk and financial risk from the generalized FGM distribution. Under some special conditions, some exact asymptotic equivalence formulas of ruin probability for finite time and asymptotically equivalent formulas for ruin probability of infinite time are obtained. In the above study, the asymptotic equivalent formula of the derived partial ruin probability has the form of linear combination, which is composed of the tail probability of insurance risk and financial risk. This equivalent formula can better reflect the impact of financial risk on insurance companies. Enrich and develop the theory of insurance risk and financial risk dependence.
【學(xué)位授予單位】：重慶理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F830;F840;O211.67

【參考文獻(xiàn)】

相關(guān)期刊論文 前4條

1 YANG Yang;LIN Jin-guan;TAN Zhong-quan;;The finite-time ruin probability in the presence of Sarmanov dependent financial and insurance risks[J];Applied Mathematics:A Journal of Chinese Universities(Series B);2014年02期

2 陳琳;劉維奇;;重尾分布族及其關(guān)系圖[J];高校應(yīng)用數(shù)學(xué)學(xué)報(bào)A輯;2009年02期

3 ;On the behavior of the product of independent random variables[J];Science in China(Series A:Mathematics);2006年03期

4 ;The Finite Time Ruin Probability with the Same Heavy-tailed Insurance and Financial Risks[J];Acta Mathematicae Applicatae Sinica(English Series);2005年01期

相關(guān)博士學(xué)位論文 前5條

1 于文廣;保險(xiǎn)風(fēng)險(xiǎn)模型的破產(chǎn)理論與分紅策略研究[D];山東大學(xué);2014年

2 李津竹;相依更新風(fēng)險(xiǎn)模型中的漸近尾行為[D];南開(kāi)大學(xué);2010年

3 蔣俊;隨機(jī)結(jié)構(gòu)中的極限定理[D];中國(guó)科學(xué)技術(shù)大學(xué);2009年

4 韋艷華;Copula理論及其在多變量金融時(shí)間序列分析上的應(yīng)用研究[D];天津大學(xué);2004年

5 劉艷;大偏差、風(fēng)險(xiǎn)理論及其在金融保險(xiǎn)中的應(yīng)用研究[D];武漢大學(xué);2004年

相關(guān)碩士學(xué)位論文 前3條

1 楊瑩瑩;相依隨機(jī)變量乘積的相關(guān)研究[D];安徽大學(xué);2012年

2 邵明陽(yáng);重尾分布理論及在保險(xiǎn)精算中的應(yīng)用研究[D];重慶理工大學(xué);2011年

3 姚兵;連續(xù)型相依風(fēng)險(xiǎn)模型破產(chǎn)概率研究[D];山東科技大學(xué);2010年

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