Distributionally Robust Optimization as a Scalable Framework to Characterize Extreme Value Distributions

TL;DR

This paper introduces a scalable distributionally robust optimization framework for extreme value distributions, improving model reliability and out-of-sample performance in multivariate EVT applications, including finance.

Contribution

It develops a novel DRO approach for multivariate EVT, combining semi-parametric max-stable constraints with convex and neural network methods, validated on synthetic and real data.

Findings

Effective recovery of prescribed characteristics from synthetic data

Enhanced out-of-sample performance compared to existing methods

Successful application to financial returns data

Abstract

The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. EVT supports using semi-parametric models called max-stable distributions built from spatial Poisson point processes. While powerful, these models are only asymptotically valid for large samples. However, since extreme data is by definition scarce, the potential for model misspecification error is inherent to these applications, thus DRO estimators are natural. In order to mitigate over-conservative estimates while enhancing out-of-sample performance, we study DRO estimators informed by semi-parametric max-stable constraints in the space of point processes. We study both tractable convex formulations for some problems of interest (e.g. CVaR) and more general neural network based estimators. Both approaches are validated using synthetically generated data, recovering prescribed characteristics, and verifying the efficacy of the proposed techniques. Additionally, the proposed method is applied to a real data set of financial returns for comparison to a previous analysis. We established the proposed model as a novel formulation in the multivariate EVT domain, and innovative with respect to performance when compared to relevant alternate proposals.