A rigorous definition of semi-Markov dependent risk model is given.This model is a generalization of the Markov dependent risk model.A criterion and necessary conditions of semiMarkov dependent risk model are obtained.The results clarify relations between elements among semi-Markov dependent risk model more clear and are applicable for Markov dependent risk model.
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.
