Seminar by Prof. Yufei Zhang from Mathematical Finance and Machine Learning, Department of Mathematics, Imperial College London

Understanding price impact is essential for designing optimal trading strategies and minimising execution costs. We consider an offline learning problem for an agent who first estimates an unknown price impact kernel from a static dataset, and then designs strategies to liquidate a risky asset while creating transient price impact. We propose a novel approach for a nonparametric estimation of the price impact kernel from a dataset containing correlated price trajectories, trading signals and metaorders. We quantify the accuracy of the estimated kernel using a metric which depends explicitly on the dataset. We show that a trader who tries to minimize her execution costs by using a greedy strategy purely based on the estimated kernel will encounter suboptimality due to spurious correlation between the trading strategy and the estimator. By adopting an offline reinforcement learning approach, we introduce a pessimistic loss functional taking the uncertainty of the estimated kernel into account, with an optimiser which eliminates the spurious correlation, and derive an asymptotically optimal bound on the execution costs even without precise information on the true kernel. Numerical experiments are included to demonstrate the effectiveness of the proposed price impact estimator and the pessimistic trading strategy.

Yufei Zhang is a Senior Lecturer in Mathematical Finance and Machine Learning at the Department of Mathematics, Imperial College London. Previously, he was an Assistant Professor in the Department of Statistics at the London School of Economics and Political Science. He earned his PhD in Mathematics from the University of Oxford in 2021. His research focuses on the intersection of stochastic control and game, machine learning, and mathematical finance. He has published in leading journals and conferences, including SIAM Journal on Control and Optimization, The Annals of Applied Probability, Journal of Machine Learning Research, and NeurIPS.