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

TL;DR

This paper extends existing ruin probability results in a Sparre Andersen insurance model with investments to include annuities and two-sided jumps, using semi-Markov process techniques.

Contribution

It introduces a novel extension of ruin probability analysis to models with annuities and two-sided jumps, building on prior work with geometric Lévy processes.

Findings

Extended ruin probability asymptotics to annuity payments.

Incorporated two-sided jumps into the ruin probability framework.

Utilized semi-Markov process techniques for the analysis.

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.