High-dimensional Statistical Arbitrage with Factor Models and Stochastic Control

Abstract

The present paper provides a study of high-dimensional statistical arbitrage that combines factor models with the tools from stochastic control, obtaining closed-form optimal strategies which are both interpretable and computationally implementable in a highdimensional setting. Our setup is based on a general statistically-constructed factor model with mean-reverting residuals, in which we show how to construct analytically marketneutral portfolios and we analyze the problem of investing optimally in continuous time and finite horizon under exponential and mean-variance utilities. We also extend our model to incorporate constraints on the investor's portfolio like dollar-neutrality and market frictions in the form of temporary quadratic transaction costs, provide extensive Monte Carlo simulations of the previous strategies with 100 assets, and describe further possible extensions of our work.