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Optimal consumption policies in illiquid markets

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Abstract

We investigate optimal consumption policies in the liquidity risk model introduced by Pham and Tankov (Math. Finance 18:613–627, 2008). Our main result is to derive smoothness C 1 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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Authors and Affiliations

  1. Dipartimento di Scienze Economiche, ed Aziendali—Facoltà di Economia, Università LUISS Guido Carli, viale Romania 32, 00197, Roma, Italy

    Alessandra Cretarola & Fausto Gozzi

  2. Laboratoire de Probabilités et Modelèles Aléatoires, CNRS, UMR 7599, Université Paris 7, and CREST-ENSAE and Institut Universitaire de France, Paris, France

    Huyên Pham

  3. Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128, Palaiseau, France

    Peter Tankov

Authors
  1. Alessandra Cretarola
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  2. Fausto Gozzi
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  3. Huyên Pham
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  4. Peter Tankov
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Corresponding author

Correspondence to Peter Tankov.

Additional information

This work is supported partly by the Europlace Institute of Finance.

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Cretarola, A., Gozzi, F., Pham, H. et al. Optimal consumption policies in illiquid markets. Finance Stoch 15, 85–115 (2011). https://doi.org/10.1007/s00780-010-0123-y

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  • DOI: https://doi.org/10.1007/s00780-010-0123-y

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