Constrained portfolio liquidation in a limit order book model

Volume 83 / 2008

Aurélien Alfonsi, Antje Fruth, Alexander Schied Banach Center Publications 83 (2008), 9-25 MSC: 91B26, 91B28, 91B70, 93E20, 60G35. DOI: 10.4064/bc83-0-1


We consider the problem of optimally placing market orders so as to minimize the expected liquidity costs from buying a given amount of shares. The liquidity price impact of market orders is described by an extension of a model for a limit order book with resilience that was proposed by Obizhaeva and Wang (2006). We extend their model by allowing for a time-dependent resilience rate, arbitrary trading times, and general equilibrium dynamics for the unaffected bid and ask prices. Our main results solve the problem of minimizing the expected liquidity costs within a given convex set of predictable trading strategies by reducing it to a deterministic optimization problem. This deterministic problem is explicitly solved for the case in which the convex set of strategies is defined via finitely many linear constraints. A detailed study of optimal portfolio liquidation in markets with opening and closing call auctions is provided as an illustration. We also obtain closed-form solutions for the unconstrained portfolio liquidation problem in our time-inhomogeneous setting and thus extend a result from our earlier paper \cite{AAA}.


  • Aurélien AlfonsiCERMICS, projet MATHFI
    École Nationale des Ponts et Chaussées
    6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne
    77455 Marne-la-Vallée, France
  • Antje FruthQuantitative Products Laboratory
    Alexanderstr. 5, 10178 Berlin, Germany
  • Alexander SchiedSchool of ORIE, Cornell University
    232 Rhodes Hall, Ithaca, NY 14853, U.S.A.

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