Paper: arXiv 2603.08553

Authors: Saeed Asadi, Jonathan Yu-Meng Li

Abstract

We propose Generative Adversarial Regression (GAR), a framework for learning conditional risk scenarios through generators aligned with downstream risk objectives. GAR builds on a regression characterization of conditional risk for elicitable functionals, including quantiles, expectiles, and jointly elicitable pairs. We extend this principle from point prediction to generative modeling by training generators whose policy-induced risk matches that of real data under the same context. To ensure robustness across all policies, GAR adopts a minimax formulation in which an adversarial policy identifies worst-case discrepancies in risk evaluation while the generator adapts to eliminate them. This structure preserves alignment with the risk functional across a broad class of policies rather than a fixed, pre-specified set. We illustrate GAR through a tail-risk instantiation based on jointly elicitable $(\mathrm{VaR}, \mathrm{ES})$ objectives. Experiments on S&P 500 data show that GAR produces scenarios that better preserve downstream risk than unconditional, econometric, and direct predictive baselines while remaining stable under adversarially selected policies.

Complexity vs Empirical Score

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

Why this score: The paper presents an innovative integration of elicitability theory, regression, and minimax generative adversarial models for tail-risk scenario generation. It effectively addresses risk misalignment in conditional generative models and demonstrates strong initial empirical results on S&P 500 data.

Research Flowchart

  flowchart TD
    A[Goal: Learn conditional risk scenarios aligned with downstream objectives] --> B[Input: Financial Data e.g., S&P 500 & Elicitable Risk Functionals]
    B --> C[Framework: Generative Adversarial Regression GAR]
    C --> D[Minimax Optimization: Adversarial policy finds worst-case risk gaps while Generator adapts]
    D --> E[Instantiation: Tail-risk generation via joint VaR and ES objectives]
    E --> F[Outcome: Generates stable scenarios that preserve downstream risk better than baselines]

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2 of 91 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.