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We consider the optimal solutions to the trade execution problem in the twodifferent classes of i) fully adapted or adaptive and ii) deterministic orstatic strategies, comparing them. We do this in two different benchmarkmodels. The first model is a discrete time framework with an information flowprocess, dealing with both permanent and temporary impact, minimizing theexpected cost of the trade. The second model is a continuous time frameworkwhere the objective function is the sum of the expected cost and a value atrisk (or expected shortfall) type risk criterion. Optimal adapted solutions areknown in both frameworks from the original works of Bertsimas and Lo (1998) andGatheral and Schied (2011). In this paper we derive the optimal staticstrategies for both benchmark models and we study quantitatively theimprovement in optimality when moving from static strategies to fully adaptedones. We conclude that, in the benchmark models we study, the difference is notrelevant, except for extreme unrealistic cases for the model or impactparameters. This indirectly confirms that in the similar framework of Almgrenand Chriss (2000) one is fine deriving a static optimal solution, as done bythose authors, as opposed to a fully adapted one, since the static solutionhappens to be tractable and known in closed form.

Static vs adapted optimal execution strategies in two benchmark trading models