Adversarial Training for Deep Hedging via Two-Budget Distributionally Robust Optimization
ORIGINAL / Adversarial Training for Deep Hedging in Nonstationary Markets
This work proposes WRAP, a framework that combines reweighting and path perturbation adversarial constraints to address market nonstationarity in deep hedging training. Its novelty lies in converting the inner distributional supremum of DRO into a tractable first-order attack, offering a more robust perturbation scheme for training policies.
01 ABSTRACT
Deep hedging learns trading policies from historical or simulated paths, but under nonstationarity these paths may not represent future markets. The authors propose WRAP based on two-budget distributionally robust optimization, allowing trajectory reweighting under a φ-divergence constraint and path perturbation under an optimal-transport constraint, and derive a first-order expansion with an explicit finite-dimensional adversarial attack. Experiments on stationary and nonstationary Heston dynamics and a generalized affine diffusion show complementary benefits from reweighting and transport, with joint adversarial training yielding the largest gains under nonstationarity.
02 KEY FINDINGS
- WRAP derives from a two-budget DRO formulation, using a weighted empirical reference distribution to balance sampling uncertainty against temporal drift.
- The ambiguity set simultaneously addresses φ-divergence reweighting and optimal-transport path perturbation as two complementary forms of distributional misspecification.
- A first-order expansion decomposes the nominal expected loss increase into a reweighting term and a transport term, yielding a tractable finite-dimensional adversarial attack.
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