High-Dimensional Statistical Arbitrage with Factor Models and Stochastic Control

Summary

The paper combines statistically constructed factor models with stochastic control to study high-dimensional statistical arbitrage. Its model assumes mean-reverting residuals and shows how to build analytically market-neutral portfolios. It then derives closed-form optimal strategies for continuous-time investing over a finite horizon under exponential and mean-variance utility criteria.

The framework also considers dollar-neutrality constraints and temporary quadratic transaction costs. Monte Carlo simulations involving 100 assets illustrate the strategies, and the authors describe possible extensions. The excerpt does not give simulation outcomes, model calibration details, or evidence from live markets, so the reported support is computational rather than empirical.

Key ideas

• The factor model represents residual returns as mean reverting.
• Analytical constructions produce market-neutral portfolios in a high-dimensional setting.
• Stochastic control yields closed-form finite-horizon strategies under exponential and mean-variance utilities.
• The framework can include dollar-neutrality and temporary quadratic transaction costs.
• Monte Carlo simulations illustrate the strategies across 100 assets.

Tags

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


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









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.