Optimal trade execution: A mean quadratic variation approach

P.A. Forsyth, J.S. Kennedy, S.T. Tse and H. Windcliff

Journal of Economic Dynamics and Control, 2012, vol. 36, issue 12, 1971-1991

Abstract: We propose the use of a mean quadratic variation criteria to determine an optimal trading strategy in the presence of price impact. We derive the Hamilton Jacobi Bellman (HJB) Partial Differential Equation (PDE) for the optimal strategy, assuming the underlying asset follows Geometric Brownian Motion (GBM) or Arithmetic Brownian Motion (ABM). The exact solution of the ABM formulation is in fact identical to the static (price-independent) approximate solution for the mean–variance objective function in Almgren and Chriss (2000). The optimal trading strategy in the GBM case is in general a function of the asset price. The static strategy determined in the ABM formulation turns out to be an excellent approximation for the GBM case, even when volatility is large.

Keywords: Optimal trading; Mean quadratic variation; HJB equation (search for similar items in EconPapers)
JEL-codes: C63 G11 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (47)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:36:y:2012:i:12:p:1971-1991

DOI: 10.1016/j.jedc.2012.05.007

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