Deep hedging is a deep-learning-based framework for derivative hedging in incomplete markets. The advantage of deep hedging lies in its ability to handle various realistic market conditions, such as market frictions, which are challenging to address within the traditional mathematical finance framework. Since deep hedging relies on market simulation, the underlying asset price process model is crucial. However, existing literature on deep hedging often relies on traditional mathematical finance models, e.g., Brownian motion and stochastic volatility models, and discovering effective underlying asset models for deep hedging learning has been a challenge. In this study, we propose a new framework called adversarial deep hedging, inspired by adversarial learning. In this framework, a hedger and a generator, which respectively model the underlying asset process and the underlying asset process, are trained in an adversarial manner. The proposed method enables to learn a robust hedger without explicitly modeling the underlying asset process. Through numerical experiments, we demonstrate that our proposed method achieves competitive performance to models that assume explicit underlying asset processes across various real market data.

翻译：深度对冲是一种基于深度学习的衍生品对冲框架，适用于非完备市场。其优势在于能够处理传统数理金融框架难以应对的现实市场条件，如市场摩擦。由于深度对冲依赖市场模拟，标的资产价格过程模型至关重要。然而，现有深度对冲文献常依赖传统数理金融模型（例如布朗运动和随机波动率模型），且寻找有效的标的资产模型用于深度对冲学习一直是个挑战。本研究受对抗性学习启发，提出了一种名为对抗深度对冲的新框架。在该框架中，对冲者与生成器分别对标的资产过程进行建模，并以对抗方式训练。所提方法无需显式建模标的资产过程即可学习鲁棒的对冲策略。通过数值实验，我们证明了该方法在多种真实市场数据中取得了与假设显式标的资产过程的模型相当的竞争力。