保险风险与金融风险相依理论研究

发布时间：2018-06-04 15:03

本文选题：保险风险和金融风险 + 广义FGM分布　；参考：《重庆理工大学》2017年硕士论文

【摘要】：近年来,风险理论一直是精算数学和应用概率研究的热门课题之一,其核心问题就是研究破产理论。因为破产理论在风险管理中具有广泛的应用价值,从而受到了国内外学者们广泛关注。随着破产理论的研究深入,在研究的时候我们需要考虑的因素也就越来越多,比如随机经济环境中的随机利率,随机投资回报率等,并且这些因素之间还存在相依关系。实际上,随着经济的发展,保险公司为了获得更多的收益,会将自己的部分资产作投资,从而,保险公司在随机经济环境中将要面临两种风险,一种是传统的理赔责任险保单组合,另一种是风险投资导致投资风险。显然,这两种风险并不独立的,而是,金融风险对保险公司的影响越来越严重。因此,研究带有保险风险与金融风险的相依风险模型更具有现实意义。在过去大量的文献利用随机过程、乘积理论、重尾分布理论等致力于研究保险风险与金融风险相互独立的情形时的破产概率渐近等价式。本文利用随机变量乘积理论、重尾分布理论等讨论离散时间的保险风险与金融风险相依问题,主要研究内容如下:首先,研究了相依随机变量乘积的尾概率问题,它们是后文研究的数学理论基础。接着,我们将推导的结论应用到保险风险研究中,我们考虑保险风险与金融风险构成的独立同分布随机向量序列服从广义FGM分布,保险风险属于(?)族,在一些特殊的条件下推得了一些精确的有限时间的破产概率渐近等价式和无限时间的破产概率渐近等价式。在上述研究中,推导的部分破产概率的渐近等价式具有线性组合的形式,该线性组合是由保险风险与金融风险尾概率构成。这样的等价式更能体现出金融风险对保险公司的影响。丰富和发展了保险风险与金融风险相依理论。
[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.
【学位授予单位】：重庆理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F830;F840;O211.67

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