Efficient simulation of tail probabilities for sums of log-elliptical risks

TL;DR

This paper introduces a new estimator for efficiently simulating the probability that the sum of dependent risks exceeds a large threshold, with proven optimal performance for log-Gaussian risks and strong results for log-elliptical risks.

Contribution

It develops a modified Asmussen-Kroese estimator for tail probability simulation, improving efficiency for log-elliptical risks in risk management.

Findings

The estimator performs optimally for log-Gaussian risks.

Numerical results show excellent performance of the proposed algorithms.

The methods effectively estimate rare event probabilities in dependent risk models.

Abstract

In the framework of dependent risks it is a crucial task for risk management purposes to quantify the probability that the aggregated risk exceeds some large value u. Motivated by Asmussen et al. (2011) in this paper we introduce a modified Asmussen-Kroese estimator for simulation of the rare event that the aggregated risk exceeds u. We show that in the framework of log-Gaussian risks our novel estimator has the best possible performance. For the more general class of log-elliptical risks with marginal distributions in the Gumbel max-domain of attraction we propose a modified Rojas-Nandayapa estimator of the rare events of interest. Numerical results demonstrate the excellent performance of our novel Asmussen-Kroese algorithm.