A Generalization of the Lundberg Condition in the Sparre Andersen Model and Some Applications

Abstract

We generalize the well-known Lundberg condition for the existence of the adjustment coefficient, R, in the Sparre Andersen model of risk theory. The new condition is given in terms of the distribution of the deficit at ruin in that model. As an application of this condition, we show that the function e Ru ψ(u) is nonincreasing when the claim size distribution in the model has a decreasing failure rate. Further, we obtain some new bounds for ruin probabilities and stop-loss premiums that are easy to compute and we give some examples to compare these bounds against existing ones in the literature.