Adversarial Training for Deep Hedging in Nonstationary Markets

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 that addresses two complementary forms of distributional misspecification. A $\phi$-divergence budget reallocates probability mass toward adverse observed scenarios, while an optimal-transport (OT) budget perturbs the scenarios themselves along locally adverse path directions. Both budgets are centered on a reference law defined by fixed baseline weights over the historical sample, chosen to balance effective sample size against temporal drift. We derive a joint first-order expansion of the resulting two-budget DRO objective whose first-order term decomposes into a reweighting term governed by the cross-scenario dispersion of hedging losses and a transport term governed by the pathwise sensitivity of the loss to trajectory perturbations. This 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 two budgets provide complementary robustness, with joint adversarial training yielding the strongest improvements in out-of-sample tail-risk performance.