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Optimal consumption policies in illiquid markets

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Author Info
Alessandra Cretarola () (Dipartimento di Scienze Economiche e Aziendali - Libera Università INTERNAZIONALE DEGLI STUDI SOCIALI G. CARLI)
Fausto Gozzi () (Dipartimento di Scienze Economiche e Aziendali - Libera Università INTERNAZIONALE DEGLI STUDI SOCIALI G. CARLI)
Huyên Pham () (PMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Pierre et Marie Curie - Paris VI - Université Denis Diderot - Paris VII, CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique)
Peter Tankov () (PMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Pierre et Marie Curie - Paris VI - Université Denis Diderot - Paris VII)

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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.

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Paper provided by HAL in its series Working Papers with number hal-00292673_v1.

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Date of creation: 02 Jul 2008
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Handle: RePEc:hal:wpaper:hal-00292673_v1

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Related research
Keywords: Illiquid market; optimal consumption; integrodifferential equations; viscosity solutions; semiconcavity; sub(super) differentials; optimal control;

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This page was last updated on 2009-11-28.


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