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A note on the dynamic liquidity trading problem with a mean-variance objective

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Abstract

This note studies the dynamic liquidity trader’s problem with a mean-variance objective function. Independent of the market impact functions and the market price dynamics, we provide a necessary and sufficient condition under which the dynamic programming equation (Bellman equation) can be extended to mean-variance objectives. Evaluation of this condition involves solving an optimization problem and taking variance of its optimal value. This computation may be difficult even when random disturbances in the market price dynamics follow a well-known distribution. To avoid this pitfall, we then provide some sufficient condition which can be assessed very easily.

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  1. David R. Cheriton School of Computer Science, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada

    Somayeh Moazeni

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  1. Somayeh Moazeni
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Correspondence to Somayeh Moazeni.

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Moazeni, S. A note on the dynamic liquidity trading problem with a mean-variance objective. Optim Lett 5, 113–124 (2011). https://doi.org/10.1007/s11590-010-0195-9

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  • DOI: https://doi.org/10.1007/s11590-010-0195-9

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