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.

Original languageEnglish
Pages (from-to)113-124
Number of pages12
JournalOptimization Letters
Volume5
Issue number1
DOIs
StatePublished - Feb 2011

Keywords

  • Dynamic programming
  • Liquidity trading
  • Price impacts

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