Bounds for the Ruin Probability of a Discrete-Time Risk Process

Abstract

We consider a discrete-time risk process driven by proportional reinsurance and an interest rate process. We assume that the interest rate process behaves as a Markov chain. To reduce the risk of ruin, we may reinsure a part or even all of the reserve. Recursive and integral equations for ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived given a stationary policy. To illustrate these results, a numerical example is included.