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Optimal Investment On Finite Horizon With Random Discrete Order Flow In Illiquid Markets

Author

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  • PAUL GASSIAT

    (Laboratoire de Probabilités et Modèles Aléatoires, University Paris Diderot, Site Chevaleret, Case 7012, 75 205 Paris Cedex 13, France)

  • HUYÊN PHAM

    (Laboratoire de Probabilités et Modèles Aléatoires, University Paris Diderot, Site Chevaleret, Case 7012, 75 205 Paris Cedex 13, France)

  • MIHAI SÎRBU

    (Department of Mathematics, University of Texas at Austin, 1 University Avenue, C1200, Austin TX78712, USA)

Abstract

We study the problem of optimal portfolio selection in an illiquid market with discrete order flow. In this market, bids and offers are not available at any time but trading occurs more frequently near a terminal horizon. The investor can observe and trade the risky asset only at exogenous random times corresponding to the order flow given by an inhomogenous Poisson process. By using a direct dynamic programming approach, we first derive and solve the fixed point dynamic programming equation satisfied by the value function, and then perform a verification argument which provides the existence and characterization of optimal trading strategies. We prove the convergence of the optimal performance, when the deterministic intensity of the order flow approaches infinity at any time, to the optimal expected utility for an investor trading continuously in a perfectly liquid market model with no-short sale constraints.

Suggested Citation

  • Paul Gassiat & Huyên Pham & Mihai Sîrbu, 2011. "Optimal Investment On Finite Horizon With Random Discrete Order Flow In Illiquid Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 17-40.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:01:n:s0219024911006243
    DOI: 10.1142/S0219024911006243
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    References listed on IDEAS

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    1. Huyên Pham & Peter Tankov, 2008. "A Model Of Optimal Consumption Under Liquidity Risk With Random Trading Times," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 613-627, October.
    2. Koichi Matsumoto, 2006. "Optimal portfolio of low liquid assets with a log-utility function," Finance and Stochastics, Springer, vol. 10(1), pages 121-145, January.
    3. Constantinos Kardaras & Eckhard Platen, 2008. "Multiplicative Approximation of Wealth Processes Involving No-Short-Sale Strategies," Research Paper Series 240, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Alessandra Cretarola & Fausto Gozzi & Huyên Pham & Peter Tankov, 2011. "Optimal consumption policies in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 85-115, January.
    Full references (including those not matched with items on IDEAS)

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