A monotonically converging algorithm for the severity of ruin in a discrete semi-markov risk model

This paper deals with the severity of ruin in a discrete semi-Markov risk model. It is shown that the work of Reinhard and Snoussi (Stochastic Models, 18) can be extended to cover the case where the premium is an integer value and no restriction on the annual result is imposed. In particular, it is shown that the severity of ruin without initial surplus is solution of a system of equations. It can be obtained by a monotonically converging algorithm when the claims are bounded.