The present paper aims to provide the first systematic study of high-dimensional statistical arbitrage using both factor models and tools from stochastic control theory, obtaining closed-form optimal strategies in most cases and extending in multiple new directions the existing literature . 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 both in continuous time and along a discrete sequence of optimally chosen deterministic times, with different utilities and finite horizon . We also discuss how to introduce various constraints on the investor's portfolio and  temporary quadratic transaction costs in both discrete and continuous time, provide Monte Carlo simulations of the previous strategies  , and describe further  extensions of our work.
The present paper aims to provide a systematic study of high-dimensional statistical arbitrage that combines factor models with the tools from stochastic control , obtaining explicit closed-form optimal strategies which are both easily 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 various constraints on the investor's portfolio 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.
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