Optimal consumption policies in illiquid markets

Alessandra Cretarola, Fausto Gozzi, Huyên Pham () and Peter Tankov
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Huyên Pham: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: We investigate optimal consumption policies in the liquidity risk model introduced in Pham and Tankov (2007). Our main result is to derive smoothness results for the value functions of the portfolio/consumption choice problem. As an important consequence, we can prove the existence of the optimal control (portfolio/consumption strategy) which we characterize both in feedback form in terms of the derivatives of the value functions and as the solution of a second-order ODE. Finally, numerical illustrations of the behavior of optimal consumption strategies between two trading dates are given.

Keywords: Illiquid market; optimal consumption; integrodifferential equations; viscosity solutions; semiconcavity; sub(super) differentials; optimal control (search for similar items in EconPapers)
Date: 2008-07-02
Note: View the original document on HAL open archive server: https://hal.science/hal-00292673v1
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Journal Article: Optimal consumption policies in illiquid markets (2011)
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