A Periodic Dividend Problem with Inconstant Barrier in Markovian Environment  

作　　者：Fang JIN Hui OU Xiang Qun YANG 

机构地区：[1]College of Mathematics and Computer Sciences, Hu'nan Normal University

出　　处：《Acta Mathematica Sinica,English Series》2015年第2期281-294,共14页数学学报（英文版）

基　　金：Supported by NSFC(Grant Nos.11171101,11271121);Doctoral Fund of Education Ministry of China(Grant No.20104306110001);Graduate Student Research Innovation Project in Hu’nan Province(Grant No.CX2013B215);the Construct Program of the Key Discipline in Hu’nan Province,Science and Technology Program of Hu’nan Province(Grant No.2014FJ3058)

摘　　要：Periodic dividend problem is a meaningful issue. Based on a compound binomial model with periodic dividend, we use a homogeneous, ergodic and irreducible discrete-time Markov chain to express the evolution from one period to the subsequent of the economic or the environmental and climatic conditions. We derive some properties about the model. A system of integral equations for the expectation and the r-th moment of discounted dividends until ruin time are obtained respectively. Moreover, by using of Contraction Mapping Principle, we solve the equation system and obtain the explicit expression.Periodic dividend problem is a meaningful issue. Based on a compound binomial model with periodic dividend, we use a homogeneous, ergodic and irreducible discrete-time Markov chain to express the evolution from one period to the subsequent of the economic or the environmental and climatic conditions. We derive some properties about the model. A system of integral equations for the expectation and the r-th moment of discounted dividends until ruin time are obtained respectively. Moreover, by using of Contraction Mapping Principle, we solve the equation system and obtain the explicit expression.

关 键 词：Periodic dividend Markovian environment inconstant barrier ruin time discounted dividends contraction mapping principle 

分 类 号：O211.62[理学—概率论与数理统计] TV641.25[理学—数学]