更新方程与保险和金融风险渐进独立下破产概率的研究

发布时间：2018-11-21 21:04

【摘要】：风险模型分为两大类：连续和离散的破产概率模型。经典风险理论相当部分是研究破产概率的，之后破产赤字及破产前瞬时盈余的引入，获得许多优美的结果，使破产概率富含更多的保险意义。文章首先研究连续破产概率模型下的更新方程。更新方程是得到破产概率的核心等式，通常是对盈余过程的数学解析而得到。文章考虑经典风险和常利率风险两种模型，从破产函数的角度出发，给出更新方程的新的推导方法：破产前瞬时盈余瑕疵密度正则化后即为破产概率；当索赔为指数分布时，，破产赤字和破产前瞬时盈余瑕疵密度正则化后的独立性。其次，文章研究了包含保险和金融风险且两者相依下的离散风险模型。此模型下，通常考虑的是保险风险X_i与金融Y_i独立的情况，因为相依的情况下随机变量积的尾分布难以处理。文章引入渐进独立刻画X i和Yi的相依性，渐进独立主要运用在极限理论中，而本文利用对其定义的扩展研究了随机变量的乘积。并利用Copula函数研究渐进独立的等价变形，列举AMH， FGM和Frank Copulas族的情况。当X i为分布属于ERV (-α,-β)和R_α时，分别给出了有限和无限时间破产概率的渐进解。
[Abstract]:Risk models are divided into two categories: continuous ruin probability model and discrete ruin probability model. The classical risk theory is mainly concerned with the probability of bankruptcy. After that, the introduction of the bankruptcy deficit and the instantaneous surplus before bankruptcy obtains many beautiful results, which makes the probability of bankruptcy rich in more insurance significance. In this paper, we first study the renewal equation under the continuous ruin probability model. The renewal equation is the core equation to obtain the ruin probability, which is usually obtained by the mathematical analysis of the surplus process. In this paper, two models of classical risk and constant interest rate risk are considered. From the point of view of ruin function, a new derivation method of renewal equation is given: the probability of ruin is obtained after the instantaneous surplus defect density is regularized before bankruptcy; When the claim is exponentially distributed, the independence of the bankruptcy deficit and the defect density of the instantaneous surplus before bankruptcy is regularized. Secondly, the discrete risk model including insurance and financial risk is studied. In this model, it is usually considered that the insurance risk X I is independent of the financial yaki, because the tail distribution of the random variable product is difficult to deal with in the case of dependence. In this paper, asymptotic independence is introduced to characterize the dependence of X I and Yi. Asymptotic independence is mainly used in the limit theory. In this paper, the product of random variables is studied by the extension of its definition. The equivalent deformation of asymptotically independent is studied by using Copula function, and the cases of AMH, FGM and Frank Copulas families are listed. When X I belongs to ERV (- 伪,-尾) and R _ 伪, the asymptotic solutions of the ruin probability of finite time and infinite time are given respectively.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;F224;O211.67

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