SIAM Journal on Financial Mathematics, Volume 11, Issue 2, Page 470-493, January 2020.
We present a method for obtaining approximate solutions to the problem of optimal execution, based on a signature method. The framework is general, only requiring that the price process is a geometric rough path and the price impact function is a continuous function of the trading speed. Following an approximation of the optimization problem, we calculate an optimal solution for the trading speed in the space of linear functions on a truncation of the signature of the price process. We provide strong numerical evidence illustrating the accuracy and flexibility of the approach. Our numerical investigation both examines cases where exact solutions are known, demonstrating that the method accurately approximates these solutions, and models where closed-form solutions of the optimal trading speed are not known. In the latter case, we obtain favorable comparisons with standard execution strategies.

中文翻译：

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具有粗糙路径签名的最佳执行

SIAM金融数学杂志，第11卷，第2期，第470-493页，2020年1月。
我们提出了一种基于签名方法获得最佳执行问题的近似解的方法。该框架是通用的，仅要求价格过程是几何粗糙的路径，并且价格影响函数是交易速度的连续函数。逼近最优化问题后，我们在截断价格过程签名的情况下，为线性函数空间中的交易速度计算了最优解。我们提供了强有力的数值证据，说明了该方法的准确性和灵活性。我们的数值研究都检查了已知精确解的情况，这表明该方法可以精确地逼近这些解，还对不知道最佳交易速度的闭式解进行了建模。在后一种情况下，