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摘要翻译：
研究了成对交易的最优交易策略，通过模型试图找到在无交易费用的情况下的最优股票份额或在有交易费用的情况下固定股票数量的最优交易时机。为了在成对交易过程中找到最优交易次数和股票数量的最优策略，我们用奇异随机控制方法研究了一个具有比例交易费用的最优成对交易问题。假设一对股票对数价格具有协整关系，考虑了具有比例交易费用的动态交易策略的投资组合优化问题。我们证明了控制问题的值函数是非线性拟变分不等式的唯一粘性解，它等价于奇异随机控制值函数的自由边界问题。然后我们发展了一个离散时间动态规划算法来计算事务区域，并证明了离散化方案的收敛性。我们用数值例子说明了我们的方法，并讨论了不同参数对交易区域的影响。本文选取了六对不同行业的美国股票进行实证研究，研究了样本外绩效，并验证了最优策略的有效性。
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英文标题：
《A singular stochastic control approach for optimal pairs trading with
proportional transaction costs》
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作者：
Haipeng Xing
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最新提交年份：
2019
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/1911.10450
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