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1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires 2 LAMSIN - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l-Ingénieur 3 CREST - Centre de Recherche en Économie et Statistique

Abstract : This paper deals with numerical solutions to an impulse control problem arising from optimal portfolio liquidation with bid-ask spread and market price impact pena\-lizing speedy execution trades. The corresponding dynamic programming DP equation is a quasi-variational inequality QVI with solvency constraint satisfied by the value function in the sense of constrained viscosity solutions. By taking advantage of the lag variable tracking the time interval between trades, we can provide an explicit backward numerical scheme for the time discretization of the DPQVI. The convergence of this discrete-time scheme is shown by viscosity solutions arguments. An optimal quantization method is used for computing the conditional expectations arising in this scheme. Numerical results are presented by examining the behaviour of optimal liquidation strategies, and comparative performance analysis with respect to some benchmark execution strategies. We also illustrate our optimal liquidation algorithm on real data, and observe various interesting patterns of order execution strategies. Finally, we provide some numerical tests of sensitivity with respect to the bid-ask spread and market impact parameters.

Keywords : Optimal liquidation Impulse control problem Quasi-variational inequality Explicit backward scheme Quantization method Viscosity solutions

Author: Fabien Guilbaud - Mohamed Mnif - Huyen Pham -



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