Optimal execution with rough path signatures

We present a method for obtaining approximate solutions to the problem of optimal execution, 5 based on a signature method. The framework is general, only requiring that the price process is a 6 geometric rough path and the price impact function is a continuous function of the trading speed. 7 Following an approximation of the optimisation problem, we calculate an optimal solution for the 8 trading speed in the space of linear functions on a truncation of the signature of the price process. 9 We provide strong numerical evidence illustrating the accuracy and flexibility of the approach. Our 10 numerical investigation both examines cases where exact solutions are known, demonstrating that 11 the method accurately approximates these solutions, and models where closed-form solutions of the 12 optimal trading speed are not known. In the latter case, we obtain favourable comparisons with 13 standard execution strategies.