带延迟的复合泊松风险模型

发布时间：2018-03-28 16:19

本文选题：风险理论　切入点：破产概率　出处：《湖南师范大学》2013年硕士论文

【摘要】：在近现代的风险理论研究中,破产理论一直是一个重要的研究对象,尤其是对经典风险模型的研究,通常假定为保费连续收取和索赔额为复合齐次Poisson过程的单险种风险模型,虽然经典风险模型及其拓广模型为描述单一险种风险模型经营提供了各种数学模式,并且得到了比较完善的结果,但是这具有一定的局限性,在现实保险市场中,随着风险经营的不断扩大,保险公司会不断投资新的险种,新的险种与旧的险种可能有关联,针对这样的情形,本文提出了带延迟的双险种复合齐次Poisson过程的三个模型,即保费常数收入双险种相互关联模型并求出了有限时间生存概率和最终破产概率的积分表达式、保费随机收入双险种不关联模型也并求出了有限时间生存概率和最终破产概率的积分表达式、保费随机收入双险种相关联模型也并求出了有限时间生存概率和最终破产概率的积分表达式。
[Abstract]:In the modern risk theory research, bankruptcy theory has been an important research object, especially the classical risk model, which is usually assumed to be a single type risk model in which the continuous premium collection and claim amount are compound homogeneous Poisson process. Although the classical risk model and its extension model provide a variety of mathematical models for describing the operation of a single insurance risk model, and obtain relatively perfect results, it has some limitations in the real insurance market. With the continuous expansion of risk management, insurance companies will continue to invest in new types of insurance, which may be related to the old ones. In view of this situation, three models of the compound homogeneous Poisson process of double insurance with delay are proposed in this paper. In this paper, the integral expressions of survival probability and ultimate ruin probability of finite time are obtained. Furthermore, the integral expressions of survival probability and ultimate ruin probability of finite time are obtained. The integral expressions of survival probability and ultimate ruin probability of finite time are also obtained.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840;O211.6

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