作为一种市场中性的交易策略, 配对交易早已被应用于各类投资实践中, 但是由于股票市场的波动性和不确定性, 配对交易依然可能存在较大的损失风险, 不过目前对带止损条件的最优阈值问题研究依然较少. 文章假定股票价格服从几何布朗运动, 在买卖两条阈值曲线的基础上, 加入止损曲线, 引入新的开仓区域. 通过最大化回报函数, 将最优阈值问题转化为随机控制问题, 求解相应的HJB方程, 得到最优阈值. 随后, 文章选取A股北京银行和华夏银行两支股票对最优阈值进行验证, 计算得到的年化收益率为14.55\%, 最大回撤相对止损前降低1.99\%, 验证了加入止损后最优阈值的有效性.

As a market-neutral trading strategy, pairs trading has been used in various investment practices. But taking into account the volatility and uncertainty of the stock market, there may still be a great risk of loss in the pairs trading. However, there is still less research on the optimal threshold problem with a stop-loss condition. This article assumes that stock prices are subject to geometric Brownian motions. We add a stop-loss curve to the original two threshold curves of buying and selling. By maximizing the reward function, the optimal thresholds problem is transformed into a stochastic control problem, and the corresponding HJB equation is solved to obtain the optimal thresholds. Subsequently, this paper selects two stocks of the Bank of Beijing and the Bank of Huaxia from a shares to verify the optimal thresholds. The calculated annualized rate of return was 14.55\%, and the maximum retracement was 1.99\% lower than that before the stop loss. It was verified that the optimal thresholds after adding the stop-loss curve were effective.