Ruin Probabilities for a Sparre Andersen Model with Investments: the Case of Annuity Payments

Abstract

This note is a complement to the paper by Eberlein, Kabanov, and Schmidt on the asymptotic of the ruin probability in a Sparre Andersen non-life insurance model with investments a risky asset whose price follows a geometric L\'evy process. Using the techniques of semi-Markov processes we extend the result of the mentioned paper to the case of annuities and models with two-sided jumps.