Monte Carlo Methods for Insurance Risk Computation

TL;DR

This paper develops Monte Carlo simulation algorithms to efficiently estimate large tail probabilities of aggregate insurance claims modeled with NEF distributions, addressing the lack of analytic solutions.

Contribution

It introduces novel importance sampling algorithms based on asymptotic analysis for tail probability estimation in insurance risk models with NEF distributions.

Findings

Algorithms effectively estimate tail probabilities for large losses.

Simulation methods outperform traditional approaches in accuracy and efficiency.

Numerical experiments validate the proposed algorithms' performance.

Abstract

In this paper we consider the problem of computing tail probabilities of the distribution of a random sum of positive random variables. We assume that the individual variables follow a reproducible natural exponential family (NEF) distribution, and that the random number has a NEF counting distribution with a cubic variance function. This specific modelling is supported by data of the aggregated claim distribution of an insurance company. Large tail probabilities are important as they reflect the risk of large losses, however, analytic or numerical expressions are not available. We propose several simulation algorithms which are based on an asymptotic analysis of the distribution of the counting variable and on the reproducibility property of the claim distribution. The aggregated sum is simulated efficiently by importancesampling using an exponential cahnge of measure. We conclude by numerical experiments of these algorithms.