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利用粗糙路径签名进行路径依赖型投资组合优化

文章 arXiv papers · 作者: Owen Futter et al.
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总结

本文介绍签名交易，这是一种投资组合优化方法，将策略表示为路径签名的线性函数。签名编码信号与资产共同变动的历史，使框架能够纳入路径依赖性并扩展传统因子模型。作者推导出动态均值方差准则和纳入回撤控制的有限期限显式解，并将所得策略与基于签名的有效前沿联系起来。

文章使用外生信号、动量和配对交易来说明该方法，示例采用合成数据和市场数据。作者认为，该方法能够保留易于解释的公式，同时处理比经典模型更丰富的时间序列模式。所提供的描述没有给出数据集、评估设计或定量表现的细节，因此仅凭本文无法评估所称优势或其稳健性。示例和框架描述的是一种建模方法，并不能证明基于签名的策略会在实盘交易中表现更好。

核心观点

  • 路径签名可以在优化模型中编码信号与资产共同变动的历史。
  • 签名交易将策略表示为路径签名的线性泛函。
  • 该框架扩展了动态均值方差优化，并纳入有限期限回撤控制。
  • 示例涵盖合成数据和市场数据上的外生信号、动量和配对交易。
  • 描述提供的信息有限，无法据此判断相对表现或实盘稳健性。

标签

投资组合构建均值回归动量配对交易风险管理
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# Signature Trading: A Path-Dependent Extension of the Mean-Variance Framework with Exogenous Signals


# Signature Trading: A Path-Dependent Extension of the Mean-Variance Framework with Exogenous Signals









In this article we introduce a portfolio optimisation framework, in which the use of rough path signatures (Lyons, 1998) provides a novel method of incorporating path-dependencies in the joint signal-asset dynamics, naturally extending traditional factor models, while keeping the resulting formulas lightweight and easily interpretable. We achieve this by representing a trading strategy as a linear functional applied to the signature of a path (which we refer to as "Signature Trading" or "Sig-Trading"). This allows the modeller to efficiently encode the evolution of past time-series observations into the optimisation problem. In particular, we derive a concise formulation of the dynamic mean-variance criterion alongside an explicit solution in our setting, which naturally incorporates a drawdown control in the optimal strategy over a finite time horizon. Secondly, we draw parallels between classical portfolio stategies and Sig-Trading strategies and explain how the latter leads to a pathwise extension of the classical setting via the "Signature Efficient Frontier". Finally, we give examples when trading under an exogenous signal as well as examples for momentum and pair-trading strategies, demonstrated both on synthetic and market data. Our framework combines the best of both worlds between classical theory (whose appeal lies in clear and concise formulae) and between modern, flexible data-driven methods that can handle more realistic datasets. The advantage of the added flexibility of the latter is that one can bypass common issues such as the accumulation of heteroskedastic and asymmetric residuals during the optimisation phase. Overall, Sig-Trading combines the flexibility of data-driven methods without compromising on the clarity of the classical theory and our presented results provide a compelling toolbox that yields superior results for a large class of trading strategies.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。