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

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Author Info

  • 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)

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    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.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 14 (2011)
    Issue (Month): 01 ()
    Pages: 17-40

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    Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:01:p:17-40

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    Related research

    Keywords: Liquidity modelling; discrete order flow; optimal investment; inhomogenous Poisson process; dynamic programming;

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    Cited by:
    1. Kazufumi Fujimoto & Hideo Nagai & Wolfgang Runggaldier, 2014. "Expected Log-Utility Maximization Under Incomplete Information and with Cox-Process Observations," Asia-Pacific Financial Markets, Springer, vol. 21(1), pages 35-66, March.

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