Finite-time ruin probabilities for the two-dimensional compound binomial model in Markovian environment

In recent years, the multi-dimensional risk model is a hot topic, and it is more realistic with the Markovian environment, which can be explained as the economic condition. In this paper, we propose the two-dimensional compound binomial model in a Markovian environment. And we obtain the explicit recursive formulae for three types of finite-time survival or ruin probabilities which are of fundamental interests in risk management by the idea for first-step and last-step consideration.