用随机控制与机器学习优化协整联动配对组合
文章 arXiv papers · 作者: Babak Mahdavi-Damghani et al.
总结
本研究比较金融数学和机器学习在连续时间、有限期限内对两种相互关联资产进行动态组合优化的方法。金融数学方法使用协整联动模型，旨在结合短期风险与长期均衡，而非依赖配对交易中常用的高相关性或协整关系。策略在均值-方差目标和幂效用目标之间动态切换；后者被表述为随机控制问题，并通过哈密顿-雅可比-贝尔曼方程和 Deep Galerkin 方法进行数值求解。
机器学习方法使用聚类定义区间，再在这些区间内进行优化。在根据同一协整联动模型生成的模拟中，作者报告称，机器学习方法优于金融数学方法。证据仅限于基于假设框架生成的数据；摘要没有提供市场数据验证、表现指标或实施细节。因此，这些结果不能证明相对优势能否延续至实盘交易或其他数据生成过程。
核心观点
- 本研究比较金融数学和机器学习在两种相互关联资产动态组合中的应用。
- 协整联动模型旨在同时表示短期风险和长期均衡。
- 金融数学策略在均值-方差方法和幂效用方法之间切换。
- 幂效用问题使用 HJB 方程和 Deep Galerkin 方法进行数值求解。
- 在同一模型生成的模拟中，基于聚类的机器学习方法优于金融数学方法。
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# Portfolio Optimization for Cointelated Pairs: SDEs vs. Machine Learning # Portfolio Optimization for Cointelated Pairs: SDEs vs. Machine Learning With the recent rise of Machine Learning as a candidate to partially replace classic Financial Mathematics methodologies, we investigate the performances of both in solving the problem of dynamic portfolio optimization in continuous-time, finite-horizon setting for a portfolio of two assets that are intertwined. In Financial Mathematics approach we model the asset prices not via the common approaches used in pairs trading such as a high correlation or cointegration, but with the cointelation model that aims to reconcile both short-term risk and long-term equilibrium. We maximize the overall P&L with Financial Mathematics approach that dynamically switches between a mean-variance optimal strategy and a power utility maximizing strategy. We use a stochastic control formulation of the problem of power utility maximization and solve numerically the resulting HJB equation with the Deep Galerkin method. We turn to Machine Learning for the same P&L maximization problem and use clustering analysis to devise bands, combined with in-band optimization. Although this approach is model agnostic, results obtained with data simulated from the same cointelation model as FM give an edge to ML.
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