Some Stable Algorithms in Ruin Theory and Their Applications

In this paper we present a stable recursive algorithm for the calculation of the probability of ultimate ruin in the classical risk model. We also present stable recursive algorithms for the calculation of the joint and marginal distributions of the surplus prior to ruin and the severity of ruin. In addition we present bounds for these distributions. Keywords: Probability of ruin; Severity of ruin; Surplus prior to ruin; Recursive calculation; Stable algorithm; Compound binomial model.