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Special Semester on Stochastics with Emphasis on Finance
Linz, September 2008 - December 2008
Presentation: A Hamilton Jacobi Bellman Approach to Optimal Trade Execution

Workshop: Computational Methods with Applications in Finance, Insurance and the Life Sciences AND Stochastic Methods in Partial Differential Equations and Applications of Deterministic and Stochastic PDEs

Time: Wed, November 19, 2008, 09:30-10:20

Speaker: Peter Forsyth

Abstract

The optimal execution problem is formulated in terms of a mean-variance tradeoff, as seen at the initial time.
The mean-variance problem can be embedded in a Linear-Quadratic optimal stochastic control problem.
A semi-Lagrangian scheme is used to solve the resulting non-linear Hamilton Jacobi Bellman (HJB) PDE. This method is essentially independent of the form for the price impact functions. We prove that the numerical scheme converges to the viscosity solution of the HJB PDE. Numerical examples are presented, in terms of the efficient trading frontier and the trading strategy. The numerical results indicate that in some cases there are many different trading strategies which generate almost identical efficient frontiers.

This work was supported by the Natural Sciences and Engineering Research Council of Canada, and by a Morgan Stanley Equity Market Microstructure Research Grant.
The views expressed herein are solely those of the authors, and not those of any other person or entity, including Morgan Stanley. Morgan Stanley is not responsible for any errors or omissions.
Nothing in the paper should be construed as a recommendation by Morgan Stanley to buy or sell any security of any kind.

Presentation slides (pdf, 217 KB)

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