Adversarial Training for Deep Hedging in Nonstationary Markets

2026-10-05

AI Summary

This study addresses the failure of deep hedging in non-stationary markets, where training trajectories cannot represent future distributions. To overcome this limitation, we propose WRAP, a framework grounded in bi-budget distributionally robust optimization that integrates trajectory reweighting with path-perturbation adversarial training. By deriving a joint first-order expansion, the in-distribution supremum is reformulated as a computable finite-dimensional attack, effectively balancing sampling uncertainty against temporal drift. Theoretically, the DRO model is constructed by combining Wasserstein optimal transport with φ-divergence constraints. Experiments on Heston and GAD models demonstrate that this joint adversarial training strategy significantly enhances hedging performance under non-stationary conditions.

Abstract

Deep hedging learns trading policies from historical or simulated market trajectories, yet under nonstationarity these training paths may not represent future market conditions. We propose WRAP (Wasserstein-Reweighting Adversarial Perturbation), a drift-aware adversarial training framework derived from a two-budget distributionally robust optimization (DRO) formulation. The formulation is anchored to a weighted empirical reference distribution whose fixed baseline weights are chosen to balance sampling uncertainty against temporal drift. Around this reference distribution, the ambiguity set addresses two complementary forms of distributional misspecification by allowing an adversary to reweight the observed trajectories subject to a $φ$-divergence constraint and perturb their paths subject to an optimal-transport (OT) constraint. We derive a joint first-order expansion in which the leading-order increase over the nominal expected loss decomposes into a reweighting contribution determined by the dispersion of hedging losses across trajectories and a transport contribution determined by the sensitivity of the loss to path perturbations. This expansion yields an explicit finite-dimensional adversarial attack that replaces the distributional inner supremum with a tractable first-order approximation. Across stationary and nonstationary Heston dynamics and a generalized affine diffusion (GAD), the experiments show complementary benefits from reweighting and transport, with joint adversarial training providing the largest gains under nonstationarity.

Problem

• Deep Hedging
• Nonstationary Markets
• Distributional Misspecification
• Temporal Drift

Innovation

• Distributionally Robust Optimization
• Adversarial Training
• Deep Hedging
• Optimal Transport
• Nonstationary Markets