重尾索赔下非平稳到达风险模型的破产概率研究

发布时间：2018-03-17 05:09

本文选题：破产概率　切入点：风险模型　出处：《安徽工程大学》2015年硕士论文　论文类型：学位论文

【摘要】：风险是风险理论的核心,风险的本质是不确定或随机的损失。经典破产论研究的是风险过程在平稳独立的假设下关于“小索赔”的情形,不适用于随机性强、索赔额大的险种,如火险、风暴险与洪水险等。经典破产论一个很强的约束是要求调节系数存在,所以次指数分布等重尾子族类成为了研究“大索赔”情形下破产概率的一种新数学工具。经典风险模型中的平稳假设条件太苛刻,与保险公司发生索赔的较强随机性的实际经营不符合,因此对于研究重尾索赔下非平稳到达过程的风险模型就特别有必要。本文从经典风险模型着手,对其索赔分布以及索赔次数过程进行推广。首先,对重尾索赔下非平稳到达的非标准延迟风险模型进行研究,利用索赔额满足重尾分布及大偏差原理,得出模型的无限时间和有限时间破产概率的渐近表达式和精细大偏差表达式。其次,对一类索赔相依的二元风险模型进行研究,考虑在风险过程中发生主、副两种索赔,利用重尾分布的性质和大偏差原理,给出了主、副索赔额均服从次指数分布下的有限时间和无限时间的破产概率与整体尾部的渐近表达式。本文是在索赔额分布为重尾分布,索赔次数过程为非平稳到达环境下建立风险模型的,完善了风险模型理论体系,符合实际,为保险经营过程中的风险评估和预测提供理论依据,具有一定的实际应用价值。最后,对本文的研究结果作了一个总结,给出了本文的展望
[Abstract]:Risk is the core of risk theory, and the essence of risk is uncertainty or random loss. For example, fire insurance, storm risk, flood risk, etc. Classical ruin theory is a strong constraint is to require the existence of adjustment coefficient, Therefore, the sub-exponential distribution of the equal-heavy tail subspecies has become a new mathematical tool for studying the ruin probability in the case of "large claims". The stationary assumptions in the classical risk model are too harsh. Therefore, it is necessary to study the risk model of non-stationary arrival process under heavy-tailed claims. First of all, the non-standard delay risk model of non-stationary arrival under heavy-tailed claim is studied, and the principle of heavy-tailed distribution and large deviation is used to satisfy the claim amount. The asymptotic expression and fine large deviation expression of infinite time and finite time ruin probability of the model are obtained. Secondly, a class of binary risk models with dependent claims are studied, and two kinds of claims are considered in the process of risk. By using the property of heavy-tailed distribution and the principle of large deviation, the asymptotic expressions of ruin probability of finite time and infinite time and global tail under the subexponential distribution of principal and secondary claims are given. In this paper, the distribution of claim amount is heavy-tailed distribution. The process of the number of claims is to establish the risk model under the non-stationary arrival environment, perfect the theoretical system of the risk model, accord with the practice, and provide the theoretical basis for the risk assessment and prediction in the process of insurance management. Finally, the research results of this paper are summarized and the prospect of this paper is given.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F272.3;F224

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