【摘要】：風(fēng)險理論是保險精算學(xué)一個重要的研究主題,其核心問題就是破產(chǎn)理論,由于其在風(fēng)險管理中廣泛的應(yīng)用價值近年來受到人們的廣泛關(guān)注.本文考慮離散時間風(fēng)險模型,假定公司處在一個隨機(jī)經(jīng)濟(jì)環(huán)境中,同時面臨兩種風(fēng)險：保險風(fēng)險與金融風(fēng)險,保險風(fēng)險即由保單引起的潛在的可靠性風(fēng)險,或潛在的理賠風(fēng)險；金融風(fēng)險即假定公司將手上的資金投入風(fēng)險市場,則由金融市場的股票價格波動等帶來的風(fēng)險.直觀上,這兩種風(fēng)險都會影響公司的破產(chǎn)概率.帶保險風(fēng)險與金融風(fēng)險的離散時間風(fēng)險模型最早由Nyrhinen[22,23]提出,隨后Tang在這一研究方向上做出了基礎(chǔ)性的工作.但他們都假定這兩種風(fēng)險是相互獨(dú)立的,這顯然與客觀實際不相符.為此,近年來,考慮一定相依結(jié)構(gòu)下帶保險風(fēng)險與金融風(fēng)險的離散時間風(fēng)險模型的破產(chǎn)理論的研究成為熱門.很多應(yīng)用概率學(xué)者都致力于定量刻畫相依結(jié)構(gòu)對公司破產(chǎn)概率的影響,顯然,這一研究工作具有十分重要的理論與實際應(yīng)用價值.本文在一些學(xué)者研究工作的基礎(chǔ)上,假定保險風(fēng)險與金融風(fēng)險服從一類廣泛的相依結(jié)構(gòu),同時假定保險風(fēng)險為次指數(shù)隨機(jī)變量,研究該相依結(jié)構(gòu)下離散時間風(fēng)險模型的有限時間破產(chǎn)概率的漸近估計.本文主要包含以下兩方面結(jié)果：(1)周知,研究一定相依結(jié)構(gòu)下帶次指數(shù)保險風(fēng)險和金融風(fēng)險的離散時間風(fēng)險模型有限時間破產(chǎn)概率的核心問題就是研究相依結(jié)構(gòu)下隨機(jī)變量乘積關(guān)于次指數(shù)族的封閉性.為此,本文第二章假定X為一實值隨機(jī)變量,Y為—正值隨機(jī)變量,且它們服從給定的相依結(jié)構(gòu),如果X是次指數(shù)的,則在一定條件下,我們證明了XY也是次指數(shù)隨機(jī)變量,從而將Tang的結(jié)果成功地推廣到相依情形.(2)考慮一定相依結(jié)構(gòu)下帶保險風(fēng)險與金融風(fēng)險的離散時間風(fēng)險模型,當(dāng)保險風(fēng)險是次指數(shù)隨機(jī)變量時,得到了有限時間破產(chǎn)概率的漸近估計,所得結(jié)果清楚反應(yīng)了相依結(jié)構(gòu)對破產(chǎn)概率的影響.特別地,當(dāng)假定保險風(fēng)險為正則變化隨機(jī)變量時,得到了有限時間破產(chǎn)概率的漸近估計的顯式表達(dá),并在一定條件下,證明了該漸近估計的一致性,從而可用于無限時刻破產(chǎn)概率的估計.
[Abstract]:Risk theory is an important research topic of insurance actuary, and its core problem is bankruptcy theory. Because of its wide application value in risk management, people pay more and more attention to it in recent years. In this paper, the discrete time risk model is considered. It is assumed that the company is in a random economic environment and faces two kinds of risks: insurance risk and financial risk, insurance risk is the potential reliability risk caused by insurance policy, or potential claim risk; Financial risk is assumed that the company will put the money into the risk market, but the financial market by the stock price fluctuations and other risks. Intuitively, these two kinds of risk can affect the company's bankruptcy probability. The discrete time risk model with insurance risk and financial risk was first put forward by Nyrhinen [22: 23], and then Tang made basic work in this research direction. But they all assume that the two risks are independent of each other, which is clearly inconsistent with objective reality. Therefore, in recent years, the research on the ruin theory of discrete time risk model with insurance risk and financial risk under certain dependent structure has become a hot topic. Many applied probabilistic scholars are devoted to quantificationally depict the influence of dependent structure on corporate bankruptcy probability. Obviously, this research work has very important theoretical and practical application value. In this paper, based on the research work of some scholars, it is assumed that insurance risk and financial risk service depend on a class of widely dependent structures, and that insurance risk is a subexponential random variable. The asymptotic estimates of the finite time ruin probability of the discrete time risk model under the dependent structure are studied. This paper mainly includes the following two results: (1) it is well known that The key problem of studying the finite time ruin probability of discrete time risk models with subexponential insurance risk and financial risk under a certain dependent structure is to study the closure of the product of random variables in dependent structures with respect to the subexponential family. Therefore, in the second chapter, we assume that X is a real valued random variable, Y is a positive random variable, and they follow a given dependent structure. If X is a subexponential variable, then under certain conditions, we prove that XY is also a subexponential random variable. Thus, the results of Tang are successfully extended to dependent cases. (2) considering the discrete time risk model with insurance risk and financial risk under certain dependent structure, when insurance risk is a sub-exponential random variable, The asymptotic estimates of the ruin probability in finite time are obtained. The results clearly reflect the effect of dependent structure on the ruin probability. In particular, when the insurance risk is assumed to be a regular variable, an explicit expression of the asymptotic estimate of the ruin probability in finite time is obtained, and the consistency of the asymptotic estimate is proved under certain conditions. Thus it can be used to estimate the ruin probability at infinite time.
【學(xué)位授予單位】：安徽大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：F840.4;F224

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