Ruin probabilities for discrete time risk models with stochastic rates of interest

Consider a discrete time risk model Un=(Un-1+Xn)(1+In)-Yn,n=1,2,..., where U0:=M>0 is the initial reserve of an insurance company, Xn the total amount of premiums, Yn the total amount of claims, In the interest rate and Un the reserve at time n. The time of ruin is denoted by [tau]M:=inf{n[greater-or-equal, slanted]1;Un