Joint and supremum distributions in the compound binomial model with Markovian environment  

作　　者：YU Yi-bin ZHANG Li-xin ZHANG Yi 

机构地区：[1]Department of Mathematics, Zhejiang University, Hangzhou 310027, China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2011年第3期265-279,共15页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China (10671176, 10771192, 70871103)

摘　　要：In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜（i.e., the time of ruin, the surplus before ruin and the deficit at ruin） by the method of mass function of up-crossing zero points, as given by Liu and Zhao （2007）. By using the same method, the recursive formula of supremum distribution is obtained. An example is included to illustrate the results of the model.In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜（i.e., the time of ruin, the surplus before ruin and the deficit at ruin） by the method of mass function of up-crossing zero points, as given by Liu and Zhao （2007）. By using the same method, the recursive formula of supremum distribution is obtained. An example is included to illustrate the results of the model.

关 键 词：Compound binomial model Markovian environment joint distribution mass function recursive formula supremum distribution. 

分 类 号：O211.62[理学—概率论与数理统计] TE373[理学—数学]