A model of optimal portfolio selection under liquidity risk and price impact |
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Authors: | Vathana Ly Vath Mohamed Mnif Huyên Pham |
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Affiliation: | (1) Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris 7, Paris, France;(2) LEGI, Ecole Polytechnique de Tunisie, Tunis, Tunisia;(3) CREST, Malakoff, France |
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Abstract: | We study a financial model with one risk-free and one risky asset subject to liquidity risk and price impact. In this market, an investor may transfer funds between the two assets at any discrete time. Each purchase or sale policy decision affects the rice of the risky asset and incurs some fixed transaction cost. The objective is to maximize the expected utility from terminal liquidation value over a finite horizon and subject to a solvency constraint. This is formulated as an impulse control problem under state constraints and we characterize the value function as the unique constrained viscosity solution to the associated quasi-variational Hamilton–Jacobi–Bellman inequality. We would like to thank Mihail Zervos for useful discussions. |
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Keywords: | Portfolio selection Liquidity risk Impulse control State constraint Discontinuous viscosity solutions |
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