Optimal Trading Strategy

Minimal Shortfall Strategies for Liquidation of a Basket of Stocks using Reinforcement Learning ArXiv ID: 2502.07868 “View on arXiv” Authors: Unknown Abstract This paper studies the ubiquitous problem of liquidating large quantities of highly correlated stocks, a task frequently encountered by institutional investors and proprietary trading firms. Traditional methods in this setting suffer from the curse of dimensionality, making them impractical for high-dimensional problems. In this work, we propose a novel method based on stochastic optimal control to optimally tackle this complex multidimensional problem. The proposed method minimizes the overall execution shortfall of highly correlated stocks using a reinforcement learning approach. We rigorously establish the convergence of our optimal trading strategy and present an implementation of our algorithm using intra-day market data. ...

A Mean Field Game between Informed Traders and a Broker ArXiv ID: 2401.05257 “View on arXiv” Authors: Unknown Abstract We find closed-form solutions to the stochastic game between a broker and a mean-field of informed traders. In the finite player game, the informed traders observe a common signal and a private signal. The broker, on the other hand, observes the trading speed of each of his clients and provides liquidity to the informed traders. Each player in the game optimises wealth adjusted by inventory penalties. In the mean field version of the game, using a Gâteaux derivative approach, we characterise the solution to the game with a system of forward-backward stochastic differential equations that we solve explicitly. We find that the optimal trading strategy of the broker is linear on his own inventory, on the average inventory among informed traders, and on the common signal or the average trading speed of the informed traders. The Nash equilibrium we find helps informed traders decide how to use private information, and helps brokers decide how much of the order flow they should externalise or internalise when facing a large number of clients. ...