Static vs adapted optimal execution strategies in two benchmark trading models

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Title: Static vs adapted optimal execution strategies in two benchmark trading models
Authors: Brigo, D
Piat, C
Item Type: Conference Paper
Abstract: We consider the optimal solutions to the trade execution problem in the two different classes of i) fully adapted or adaptive and ii) deterministic or static strategies, comparing them. We do this in two different benchmark models. The first model is a discrete time framework with an information flow process, dealing with both permanent and temporary impact, minimizing the expected cost of the trade. The second model is a continuous time framework where the objective function is the sum of the expected cost and a value at risk (or expected shortfall) type risk criterion. Optimal adapted solutions are known in both frameworks from the original works of Bertsimas and Lo (1998) and Gatheral and Schied (2011). In this paper we derive the optimal static strategies for both benchmark models and we study quantitatively the improvement in optimality when moving from static strategies to fully adapted ones. We conclude that, in the benchmark models we study, the difference is not relevant, except for extreme unrealistic cases for the model or impact parameters. This indirectly confirms that in the similar framework of Almgren and Chriss (2000) one is fine deriving a static optimal solution, as done by those authors, as opposed to a fully adapted one, since the static solution happens to be tractable and known in closed form.
Date of Acceptance: 15-Feb-2018
Publisher: World Scientific Publishing Co.
Journal / Book Title: Innovations in Insurance, Risk- and Asset Management
Copyright Statement: This paper is embargoed until publication.
Conference Name: Innovations in Insurance, Risk- and Asset Management
Keywords: q-fin.PR
60H10, 60J60, 91B70
Publication Status: Accepted
Start Date: 2018-04-05
Finish Date: 2018-04-07
Conference Place: Munich, Germany
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Financial Mathematics
Faculty of Natural Sciences

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