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

Paper: arXiv 2408.00131

Authors: Patrick Kuiper, Ali Hasan, Wenhao Yang, Yuting Ng, Hoda Bidkhori, Jose Blanchet, Vahid Tarokh

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a highly novel and mathematically sophisticated extension of distributionally robust optimization (DRO) to multivariate Extreme Value Theory (EVT) via Wasserstein metrics on spatial Poisson point processes. Empirical validation is solid, leveraging both challenging synthetic stress-tests and real financial return data, though providing open-source code would further enhance reproducibility.

Research Flowchart

  flowchart TD
    A[Research Goal: Scalable DRO Framework for Multidimensional EVT] --> B[Input Data: Synthetic Data & Real Financial Returns]
    B --> C[Methodology: DRO Informed by Max-Stable Constraints in Point Processes]
    C --> D1[Tractable Convex Formulations e.g., CVaR]
    C --> D2[General Neural Network Estimators]
    D1 --> E[Validation & Evaluation: Out-of-Sample Performance]
    D2 --> E
    E --> F[Outcomes: Mitigated Over-Conservatism & Novel Multivariate EVT Baseline]

Cited References (21)

1. Distributionally Robust Inference for Extreme Value-at-Risk (2020) — link
2. Modelling Extreme Multivariate Events (1991)
3. A Spectral Representation for Max-stable Processes (1984) — link
4. Stein’s method and point process approximation (1992)
5. Stein’s method, Palm theory and Poisson process approximation (2004)
6. Distributionally robust stochastic optimization with Wasserstein distance (2023)
7. Exact simulation of max-stable processes (2016)
8. Quantifying distributional model risk via optimal transport (2019)

0 of 21 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.