Optimal trade execution with unknown drift

Martin Forde

Journal of Risk

Abstract: We show how existing results for optimal trading strategies with linear temporary price impact, exponential resilience or proportional transaction costs can be easily adapted for the more realistic situation in which the drift of the asset is unknown and we need to project to the observable filtration generated by the asset price process using results from nonlinear filtering theory. In particular, we observe that an arithmetic Brownian motion P with unknown (constant) drift μ is the continuation of a generalized bridge process under ƑP, with the true drift replaced with its unbiased estimate over a fixed time window.

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