# High-dimensional statistical arbitrage with factor models and stochastic control

## TL;DR

This paper develops a high-dimensional statistical arbitrage framework combining factor models and stochastic control, providing explicit strategies for market-neutral portfolios with practical constraints and extensive simulations.

## Contribution

It introduces a novel analytical approach to high-dimensional arbitrage using factor models and stochastic control, including handling constraints and transaction costs.

## Key findings

- Closed-form optimal strategies for high-dimensional portfolios.
- Effective incorporation of constraints like dollar-neutrality.
- Successful Monte Carlo simulations with 100 assets.

## 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 high-dimensional setting. Our setup is based on a general statistically-constructed factor model with mean-reverting residuals, in which we show how to construct analytically market-neutral 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.