Optimal consumption policies in illiquid markets |
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| Authors: | Alessandra Cretarola Fausto Gozzi Huyên Pham Peter Tankov |
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| Institution: | 1.Dipartimento di Scienze Economiche, ed Aziendali—Facoltà di Economia,Università LUISS Guido Carli,Roma,Italy;2.Laboratoire de Probabilités et Modelèles Aléatoires, CNRS, UMR 7599, Université Paris 7, and CREST-ENSAE and Institut Universitaire de France,Paris,France;3.Centre de Mathématiques Appliquées,Ecole Polytechnique,Palaiseau,France |
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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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| Keywords: | |
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