HEDGE-FUND MANAGEMENT WITH LIQUIDITY CONSTRAINT

Hugo E. Ramirez, Peter Duck (), Paul V. Johnson () and Sydney Howell ()
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Hugo E. Ramirez: Faculty of Economics, Universidad del Rosario, Calle 12C No. 6-25 Bogotá, COL
Peter Duck: #x2020;School of Mathematics, The University of Manchester, Oxford road, Manchester, M13 9PL, UK
Paul V. Johnson: #x2020;School of Mathematics, The University of Manchester, Oxford road, Manchester, M13 9PL, UK
Sydney Howell: #x2021;Business School, The University of Manchester, Oxford road, Manchester, M13 9PL, UK

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 06, 1-31

Abstract: We propose a model for a manager of a hedge fund with a liquidity constraint, where he is seeking to optimize his utility of wealth, with one and multiple period horizons. By using stochastic control techniques, we state the corresponding multi-dimensional Hamilton–Jacobi–Bellman partial differential equation and we use a robust numerical approximation to obtain its unique viscosity solution. We examine the effects of the liquidity constraint on managerial trading decisions and optimal allocation, finding that the manager behaves in a less risky manner. We also calculate the cost of being at sub-optimal positions as the difference in the certainty equivalent payoff for the manager. Moreover, we compare the values of a benchmark hedge fund with another one having a risky asset with a higher rate of return but less liquidity, finding that higher rate of return with a liquidity constraint does not always lead to greater return.

Keywords: Hedge-fund management; stochastic control; liquidity; semi-Lagrangian; finite differences (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0219024919500262

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