OPTIMAL INVESTMENT ON FINITE HORIZON WITH RANDOM DISCRETE ORDER FLOW IN ILLIQUID MARKETS

Paul Gassiat (), Huyên Pham () and Mihai Sîrbu ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2011, vol. 14, issue 01, 17-40

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.

Keywords: Liquidity modelling; discrete order flow; optimal investment; inhomogenous Poisson process; dynamic programming (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1142/S0219024911006243

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