Optimal trade execution: A mean quadratic variation approach
AbstractWe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Dynamics and Control.
Volume (Year): 36 (2012)
Issue (Month): 12 ()
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Web page: http://www.elsevier.com/locate/jedc
Optimal trading; Mean quadratic variation; HJB equation;
Find related papers by JEL classification:
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
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