一类带阈值分红策略下相依风险模型的Gerber-Shiu折现罚金函数

发布时间：2018-11-17 18:22

【摘要】：本文致力于研究一类新的阈值分红策略下相依双险种更新风险模型的折现罚金函数的一些性质。 Lundberg-Cramer经典风险模型提出以来,很多学者不断对其进行推广和完善,使模型更加符合保险公司的实际运营情况。时至今日已经提出研究了数十种不同类型的风险模型。随着国内保险业的不断发展成熟,保险市场的竞争日趋激烈,多险种业务已经成为保险公司的主流业务,并且很多险种之间是相互依存,互相关联的,所以研究有相依关系的多险种风险模型具有非常重要的现实意义和应用前景。本文简单介绍了一下风险模型的演变历史和主要结果,并在前人工作的基础上,建立了一个阈值分红策略下相依双险种更新风险模型,研究了其Gerber-Shiu折现罚金函数的一些性质,得出了该模型下折现罚金函数满足的积分微分方程,并给出在保险公司初始盈余为0时的破产概率Ψ(0)的表达式,进一步推导了Gerber-Shiu折现罚金函数满足的更新方程。
[Abstract]:In this paper, we study some properties of discounted penalty function for renewal risk model of dependent double insurance under a new threshold dividend policy. Since the classical risk model of Lundberg-Cramer was put forward, many scholars have been popularizing and perfecting it, which makes the model more in line with the actual operation of insurance companies. So far, dozens of different types of risk models have been proposed. With the continuous development of the domestic insurance industry, the competition in the insurance market is becoming increasingly fierce, multi-insurance business has become the mainstream business of insurance companies, and many types of insurance are interdependent and interrelated. Therefore, it is of great practical significance and application prospect to study the multi-insurance risk model with dependent relationship. In this paper, the evolution history and main results of risk model are briefly introduced, and based on the previous work, a risk model of dependent double insurance renewal under threshold dividend strategy is established. In this paper, we study some properties of Gerber-Shiu discounted penalty function, obtain the integro-differential equation of discounted penalty function under this model, and give the expression of ruin probability 蠄 (0) when the initial surplus of insurance company is 0. Furthermore, the renewal equation of Gerber-Shiu discounted penalty function is derived.
【学位授予单位】：中央民族大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F840.3;O211.67

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