A duality approach to the worst case value at risk for a sum of dependent random variables with known covariances

TL;DR

This paper introduces a duality-based method to estimate worst-case Value at Risk for sums of dependent variables using covariance data, avoiding parametric copula models.

Contribution

It presents a novel approach that derives bounds on worst-case VaR using only covariances, leveraging duality theory without relying on specific copula assumptions.

Findings

Provides bounds on worst-case VaR for dependent variables

Uses duality theory for infinite-dimensional linear programs

Avoids parametric copula assumptions

Abstract

We propose an approach to the aggregation of risks which is based on estimation of simple quantities (such as covariances) associated to a vector of dependent random variables, and which avoids the use of parametric families of copulae. Our main result demonstrates that the method leads to bounds on the worst case Value at Risk for a sum of dependent random variables. Its proof applies duality theory for infinite dimensional linear programs.