提出一种可扩展的路径依赖对冲算法，无需假设市场模型。
Rough kernel hedging
- 基于算子值核与未截断签名核，构建可证明收敛的对冲方法。
- 在广义损失函数下获得解析解，保证全局最优解存在唯一。
- 支持融合交易信号等特征，贴近实际机器学习对冲场景。
基于算子值核与未截断签名核的泛函分析框架，我们提出一种适用于高维、路径依赖对冲问题的可扩展且可证明收敛的签名基算法。通过将市场动态建模为一般的几何粗糙路径，我们实现完全模型无关的方法。此外，借助表示定理，我们为所得到的优化问题提供了全局最小值存在性与唯一性的理论保证，并在高度通用的损失函数下推导出解析解。与流行的深度对冲方法类似，但更具理论严谨性，该方法可通过底层算子值核纳入额外特征，如交易信号、新闻分析和过往对冲决策，紧密贴合真实机器学习实践。
原文摘要 · Abstract (English)
Building on the functional-analytic framework of operator-valued kernels and un-truncated signature kernels, we propose a scalable, provably convergent signature-based algorithm for a broad class of high-dimensional, path-dependent hedging problems. We make minimal assumptions about market dynamics by modelling them as general geometric rough paths, yielding a fully model-free approach. Furthermore, through a representer theorem, we provide theoretical guarantees on the existence and uniqueness of a global minimum for the resulting optimization problem and derive an analytic solution under highly general loss functions. Similar to the popular deep hedging approach, but in a more rigorous fashion, our method can also incorporate additional features via the underlying operator-valued kernel, such as trading signals, news analytics, and past hedging decisions, closely aligning with true machine-learning practice.
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