A convex duality method for optimal liquidation with participation constraints

Olivier Guéant, Jean-Michel Lasry and Jiang Pu
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Jean-Michel Lasry: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

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Abstract: In spite of the growing consideration for optimal execution issues in the financial mathematics literature, numerical approximations of optimal trading curves are almost never discussed. In this article, we present a numerical method to approximate the optimal strategy of a trader willing to unwind a large portfolio. The method we propose is very general as it can be applied to multi-asset portfolios with any form of execution costs, including a bid-ask spread component, even when participation constraints are imposed. Our method, based on convex duality, only requires Hamiltonian functions to have C^{1,1} regularity while classical methods require additional regularity and cannot be applied to all cases found in practice.

Date: 2015
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Published in Market microstructure and liquidity, 2015, 1 (1), ⟨10.1142/S2382626615500021⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01393127

DOI: 10.1142/S2382626615500021

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