Efficient simulation of ruin probabilities when claims are mixtures of heavy and light tails

TL;DR

This paper introduces an efficient simulation method for ruin probabilities in risk models with mixed claim size distributions, combining geometric representations and control variates to improve accuracy and computational efficiency.

Contribution

It develops a novel control variate technique using a geometric compound representation for simulating ruin probabilities with mixed heavy and light tails.

Findings

Significant variance reduction achieved with the new method.

Performance comparable or superior to classical Pollaczek-Khinchine based techniques.

Effective for both small and large initial capital scenarios.

Abstract

We consider the classical Cram\'er-Lundberg risk model with claim sizes that are mixtures of phase-type and subexponential variables. Exploiting a specific geometric compound representation, we propose control variate techniques to efficiently simulate the ruin probability in this situation. The resulting estimators perform well for both small and large initial capital. We quantify the variance reduction as well as the efficiency gain of our method over another fast standard technique based on the classical Pollaczek-Khinchine formula. We provide a numerical example to illustrate the performance, and show that for more time-consuming conditional Monte Carlo techniques, the new series representation also does not compare unfavorably to the one based on the Pollaczek- Khinchine formula.