Double-markov risk model

Given a new Double-Markov risk model DM=(μ,Q,ν,H;Y,Z) and Double-Markov risk process U={U(t),t≥ 0}. The ruin or survival problem is addressed. Equations which the survival probability satisfied and the formulas of calculating survival probability are obtained. Recursion formulas of calculating the survival probability and analytic expression of recursion items are obtained. The conclusions are expressed by Q matrix for a Markov chain and transition probabilities for another Markov Chain.