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

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.