An Integrated Approach to Importance Sampling and Machine Learning for Efficient Monte Carlo Estimation of Distortion Risk Measures in Black Box Models

TL;DR

This paper introduces a machine learning-enhanced importance sampling method to efficiently estimate distortion risk measures in complex, black-box simulation models, significantly reducing computational costs for risk assessment.

Contribution

It presents a novel integrated approach combining importance sampling and machine learning to improve Monte Carlo estimation of distortion risk measures in expensive models.

Findings

The method reduces computational costs in risk estimation.

Numerical experiments demonstrate improved efficiency and accuracy.

Applicable to various distortion risk measures and models.

Abstract

Distortion risk measures play a critical role in quantifying risks associated with uncertain outcomes. Accurately estimating these risk measures in the context of computationally expensive simulation models that lack analytical tractability is fundamental to effective risk management and decision making. In this paper, we propose an efficient important sampling method for distortion risk measures in such models that reduces the computational cost through machine learning. We demonstrate the applicability and efficiency of the Monte Carlo method in numerical experiments on various distortion risk measures and models.