An importance sampling approach for copula models in insurance

TL;DR

This paper introduces an importance sampling method for copula models in insurance, enhancing Monte Carlo estimators especially for tail-dependent scenarios, with significant variance reduction demonstrated in a case study.

Contribution

It presents two novel algorithms for importance sampling in copula models, optimizing proposal distributions to reduce sampling error in insurance and finance applications.

Findings

Variance reduction factors between 10 and 30.

Algorithms applicable to all copula classes with feasible sampling.

Effective in tail-dependent probability estimation.

Abstract

An importance sampling approach for sampling copula models is introduced. We propose two algorithms that improve Monte Carlo estimators when the functional of interest depends mainly on the behaviour of the underlying random vector when at least one of the components is large. Such problems often arise from dependence models in finance and insurance. The importance sampling framework we propose is general and can be easily implemented for all classes of copula models from which sampling is feasible. We show how the proposal distribution of the two algorithms can be optimized to reduce the sampling error. In a case study inspired by a typical multivariate insurance application, we obtain variance reduction factors between 10 and 30 in comparison to standard Monte Carlo estimators.