  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.

Mathematical Finance