Time in the red in a two state Markov model

Consider a discrete time risk process based on a two state Markov chain. The premium is assumed to be the reciprocal of an integer, the benefit is unity and the initial surplus is a multiple of the premium. We will derive recursion formulae for the joint distribution of ruin and severity of ruin and for the expected time to surplus zero from a given negative surplus. Further we will derive asymptotic estimates for the ruin probability, the severity of ruin and their joint distribution. In conclusion we will calculate the expected time in the red.