Upper bounds for ruin probabilities in an autoregressive risk model with a Markov chain interest rate

In this paper, ruin probabilities are examined in a discrete timerisk model in which the interest rates follow a Markov chain with adenumerable state space and the net losses(the claim amount minusthe premium income) are assumed to have a dependent AR(1) structure.An upper bound for ultimate ruin probability is obtained bymartingale approach. Recursive equations for both finite time ruinprobabilities and ultimate ruin probability are derived. Byintegrating the inductive method and the recursive equation, anupper bound is given for both finite time ruin probabilities andultimate ruin probability.