Ruin Probabilities for a Sparre Andersen Model with Investments

TL;DR

This paper analyzes the ruin probabilities in a Sparre Andersen model with investments, showing that the asymptotic behavior mainly depends on the properties of the risky asset's price process, modeled as a geometric Lévy process.

Contribution

It introduces a model combining a compound renewal process with investments in a geometric Lévy process, highlighting the dominant influence of the asset's properties on ruin probabilities.

Findings

Ruin probability asymptotics depend primarily on the price process characteristics.

The model integrates investment strategies into classical ruin theory.

The geometric Lévy process significantly influences the ruin behavior.

Abstract

We study a Sparre Andersen model in which the business activity of the company is described by a compound renewal process with drift assuming that the capital reserves are invested in a risky asset. The price of the latter is assumed to evolve according to a geometric L\'evy process. We prove that the asymptotic behavior of the ruin probability depends to a large extent only on the properties of the price process.