带次指数保险风险相依离散风险模型的破产理论及相关问题
发布时间：2019-02-23 13:06
【摘要】：风险理论是保险精算学一个重要的研究主题,其核心问题就是破产理论,由于其在风险管理中广泛的应用价值近年来受到人们的广泛关注.本文考虑离散时间风险模型,假定公司处在一个随机经济环境中,同时面临两种风险：保险风险与金融风险,保险风险即由保单引起的潜在的可靠性风险,或潜在的理赔风险；金融风险即假定公司将手上的资金投入风险市场,则由金融市场的股票价格波动等带来的风险.直观上,这两种风险都会影响公司的破产概率.带保险风险与金融风险的离散时间风险模型最早由Nyrhinen[22,23]提出,随后Tang在这一研究方向上做出了基础性的工作.但他们都假定这两种风险是相互独立的,这显然与客观实际不相符.为此,近年来,考虑一定相依结构下带保险风险与金融风险的离散时间风险模型的破产理论的研究成为热门.很多应用概率学者都致力于定量刻画相依结构对公司破产概率的影响,显然,这一研究工作具有十分重要的理论与实际应用价值.本文在一些学者研究工作的基础上,假定保险风险与金融风险服从一类广泛的相依结构,同时假定保险风险为次指数随机变量,研究该相依结构下离散时间风险模型的有限时间破产概率的渐近估计.本文主要包含以下两方面结果：(1)周知,研究一定相依结构下带次指数保险风险和金融风险的离散时间风险模型有限时间破产概率的核心问题就是研究相依结构下随机变量乘积关于次指数族的封闭性.为此,本文第二章假定X为一实值随机变量,Y为—正值随机变量,且它们服从给定的相依结构,如果X是次指数的,则在一定条件下,我们证明了XY也是次指数随机变量,从而将Tang的结果成功地推广到相依情形.(2)考虑一定相依结构下带保险风险与金融风险的离散时间风险模型,当保险风险是次指数随机变量时,得到了有限时间破产概率的渐近估计,所得结果清楚反应了相依结构对破产概率的影响.特别地,当假定保险风险为正则变化随机变量时,得到了有限时间破产概率的渐近估计的显式表达,并在一定条件下,证明了该渐近估计的一致性,从而可用于无限时刻破产概率的估计.
[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.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F840.4;F224
[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.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F840.4;F224
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