文献类型：期刊文献

中文题名：Erlang(2)过程的风险分析与美式看跌期权

英文题名：Ruin Analysis for Erlang(2) Risk Process and American Put Option

作者：丁钊鹏[1]

第一作者：丁钊鹏

机构：[1]北京联合大学商务学院

第一机构：北京联合大学商务学院

年份：2006

卷号：22

期号：4

起止页码：372-386

中文期刊名：应用概率统计

外文期刊名：Chinese Journal of Applied Probability and Statistics

收录：CSTPCD;;北大核心:【北大核心2004】；CSCD:【CSCD2011_2012】；

语种：中文

中文关键词：Erlang(2)过程;古典风险模型;破产时刻;美式看跌期权

摘要：在经典的风险理论中涉及到的索赔风险是服从复合Poission过程的,与之不同,我们考虑Er- lang(2)风险过程．Erlang(2)分布往往见诸于控制理论中,这里它作为索赔发生间隔时间的分布被引入了．本文中,我们介绍一个与破产时刻、破产前时刻的盈余以及破产时刻赤字有关的辅助函数φ(·),函数中涉及的这三个变量对风险模型的研究都是最基本也是最重要的．Willmot and Lin (1999)曾在古典连续时间风险模型之中研讨过这一函数．受Gerber and Shiu(1997)及Willmot and Lin(2000)在古典模型下的研究过程的启发,本文的一个重要结果就是找到破产前时刻的盈余以及破产时刻赤字的联合分布密度函数．更得益于Gerber and Landry(1998)及Gerber and Shiu (1999)的思想,我们应用以上的结果去寻求基础资产服从一定风险资产价格过程的美式看跌期权最优交易策略．
In the classical risk theory, the risk of the accumulative claims follows Poission process. We will consider Erlang（2） risk process with the time between two claims.following Erlang（2） distribution which always appears in control theory. In this paper, we consider an auxiliary function Ф（·）which involves the time of ruin, the surplus immediately before ruin, and the deficit at the time of ruin for our model within the three variables are essential and principal for the study of risk process. This auxiliary function has been studied by Willmot and Lin （1999） in the classical continuous time risk model. Motivated by the exposition in Gerber and Shiu （1997） and Willmot and Lin （2000）, the first important result is to find the joint distribution density function of U（T-） and ｜U（T）｜ which is convenient to get the expression of Ф（·）. But our approach is rather different from the technique for the classical risk model because of the distinct internal characteristic between two models. Influenced by the ideas in Gerber and Landry （1998） and Gerber and Shiu （1999）, we will determine the optimal exercise price for an American put option whose foundation property price follows some risk process as an application.