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.
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)
