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摘要翻译：
本文研究了一个成对交易规则。这个想法是监控两种历史上相关的证券。当背离发生时，即一只股票上涨而另一只股票下跌，就进入了一对交易，由一对股票做空表现好的股票和做多表现差的股票组成。这种策略押注于两者之间的“利差”最终会收敛。本文用均值回归模型来控制对的差值。目标是交易这对组合，以最大化整体回报。每笔交易收取固定的佣金费用。此外，止损限额作为一种状态约束被施加。用关联的HJB方程（拟变分不等式）来刻画值函数。结果表明，最优停止问题的解可以通过求解若干拟代数方程组得到。我们根据一个验证定理给出了一组充分条件。数值算例证明了这一结果。
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英文标题：
《An Optimal Pairs-Trading Rule》
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作者：
Qingshuo Song, Qing Zhang
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最新提交年份：
2013
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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英文摘要：
This paper is concerned with a pairs trading rule. The idea is to monitor two historically correlated securities. When divergence is underway, i.e., one stock moves up while the other moves down, a pairs trade is entered which consists of a pair to short the outperforming stock and to long the underperforming one. Such a strategy bets the "spread" between the two would eventually converge. In this paper, a difference of the pair is governed by a mean-reverting model. The objective is to trade the pair so as to maximize an overall return. A fixed commission cost is charged with each transaction. In addition, a stop-loss limit is imposed as a state constraint. The associated HJB equations (quasi-variational inequalities) are used to characterize the value functions. It is shown that the solution to the optimal stopping problem can be obtained by solving a number of quasi-algebraic equations. We provide a set of sufficient conditions in terms of a verification theorem. Numerical examples are reported to demonstrate the results.
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PDF链接：
https://arxiv.org/pdf/1302.6120
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