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

Author

Listed:
  • 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.

Suggested Citation

  • Patrick Kuiper & Ali Hasan & Wenhao Yang & Yuting Ng & Hoda Bidkhori & Jose Blanchet & Vahid Tarokh, 2024. "Distributionally Robust Optimization as a Scalable Framework to Characterize Extreme Value Distributions," Papers 2408.00131, arXiv.org.
  • Handle: RePEc:arx:papers:2408.00131
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    References listed on IDEAS

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    1. Yuen, Robert & Stoev, Stilian & Cooley, Daniel, 2020. "Distributionally robust inference for extreme Value-at-Risk," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 70-89.
    2. Marcon, Giulia & Padoan, Simone & Naveau, Philippe & Muliere, Pietro & Segers, Johan, 2017. "Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials," LIDAM Reprints ISBA 2017003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Clément Dombry & Sebastian Engelke & Marco Oesting, 2016. "Exact simulation of max-stable processes," Biometrika, Biometrika Trust, vol. 103(2), pages 303-317.
    4. Jose Blanchet & Karthyek Murthy, 2019. "Quantifying Distributional Model Risk via Optimal Transport," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 565-600, May.
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