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含交易成本配对交易的奇异随机控制

文章 arXiv papers · 作者: Haipeng Xing
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总结

本研究将配对交易表述为两个协整股票对数价格的投资组合优化问题。奇异随机控制模型在计入比例交易成本的同时，联合决定交易时机和调整的股数。价值函数被刻画为非线性拟变分不等式的唯一黏性解，也可以表示为自由边界问题。

为进行计算，作者开发了一种离散时间动态规划方法来识别交易区域，并报告称离散化方案具有收敛性。数值示例考察了参数选择对这些区域的影响。一项样本外实证研究使用了来自不同行业的六对美国股票，并将结果作为策略有效性的证据。本文没有提供绩效数据或详细的执行假设，而且结果取决于协整模型和所选股票对；这些结果本身不能证明该方法具有广泛适用性或实盘表现。

核心观点

  • 模型假设两个股票对数价格之间存在协整关系。
  • 奇异随机控制在比例成本下联合优化交易时机与股数调整。
  • 该控制问题由非线性拟变分不等式和自由边界形式刻画。
  • 离散时间动态规划方案用于计算交易区域，作者报告称该方案具有收敛性。
  • 实证评估使用来自不同行业的六对美国股票进行样本外测试。

标签

股票配对交易统计学投资组合构建美国市场
全文
# A singular stochastic control approach for optimal pairs trading with proportional transaction costs


# A singular stochastic control approach for optimal pairs trading with proportional transaction costs









Optimal trading strategies for pairs trading have been studied by models that try to find either optimal shares of stocks by assuming no transaction costs or optimal timing of trading fixed numbers of shares of stocks with transaction costs. To find optimal strategies which determine optimally both trade times and number of shares in pairs trading process, we use a singular stochastic control approach to study an optimal pairs trading problem with proportional transaction costs. Assuming a cointegrated relationship for a pair of stock log-prices, we consider a portfolio optimization problem which involves dynamic trading strategies with proportional transaction costs. We show that the value function of the control problem is the unique viscosity solution of a nonlinear quasi-variational inequality, which is equivalent to a free boundary problem for the singular stochastic control value function. We then develop a discrete time dynamic programming algorithm to compute the transaction regions, and show the convergence of the discretization scheme. We illustrate our approach with numerical examples and discuss the impact of different parameters on transaction regions. We study the out-of-sample performance in an empirical study that consists of six pairs of U.S. stocks selected from different industry sectors, and demonstrate the efficiency of the optimal strategy.

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。