发表机构
University of Waterloo; EPFL（滑铁卢大学; 洛桑联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非平稳市场，提出基于两预算DRO的WRAP对抗训练框架，通过重加权和路径扰动联合优化，提升深度对冲策略的鲁棒性，实验验证其在非平稳下增益最大。
AI 中文摘要
深度对冲从历史或模拟市场轨迹中学习交易策略，然而在非平稳条件下，这些训练路径可能无法代表未来的市场状况。我们提出了WRAP（Wasserstein重加权对抗扰动），一种基于两预算分布鲁棒优化（DRO）公式的漂移感知对抗训练框架。该公式锚定于一个加权经验参考分布，其固定的基线权重被选择以平衡采样不确定性与时间漂移。在此参考分布周围，模糊集通过允许对手在φ散度约束下对观测轨迹进行重加权，并在最优传输（OT）约束下扰动其路径，来解决两种互补形式的分布误设。我们推导了一个联合一阶展开，其中名义期望损失上的前导阶增加分解为一个重加权贡献（由对冲损失在各轨迹间的离散度决定）和一个传输贡献（由损失对路径扰动的敏感性决定）。该展开产生了一个显式的有限维对抗攻击，用可处理的一阶近似替代了分布内上确界。在平稳和非平稳Heston动态以及广义仿射扩散（GAD）的实验中，结果表明重加权和传输具有互补优势，联合对抗训练在非平稳条件下提供了最大的收益。
英文摘要
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.
