Optimal Microstructure Trading with a Long-Term Utility Function

26 Pages Posted: 24 Oct 2017 Last revised: 3 Dec 2017

See all articles by Elie Benveniste

Elie Benveniste

New York University (NYU) - Courant Institute of Mathematical Sciences

Gordon Ritter

New York University (NYU) - Courant Institute of Mathematical Sciences; City University of New York (CUNY) - Weissman School of Arts and Sciences; Columbia University - Department of Mathematics; University of Chicago - Department of Mathematics; Columbia University - School of Professional Studies

Date Written: December 2, 2017

Abstract

We combine Almgren--Chriss optimal execution with market microstructure in a framework where passive (joining the queue in a limit order book) or aggressive (willing to cross the bid-offer spread) modes of execution are allowed. To achieve this, we represent the Almgren--Chriss strategy within the framework of Hamiltonian dynamics. We then show that if a risk-neutral agent has expected returns equal to Hamilton's generalized momenta, then such agent repeatedly solving a myopic wealth-maximization problem reproduces the Almgren and Chriss solution. Hence the vector of generalized momenta, p, represents effective microstructure alphas, and also is the gradient of the Bellman value function. We demonstrate that our formulation is computationally efficient and provide a practical algorithm, accompanied by a numerical example which illustrates what can go wrong in the naive approach.

Keywords: Finance, Investment Analysis, Optimal Execution, Market Microstructure

JEL Classification: C61,G11

Suggested Citation

Benveniste, Elie and Ritter, Gordon, Optimal Microstructure Trading with a Long-Term Utility Function (December 2, 2017). Available at SSRN: https://ssrn.com/abstract=3057570 or http://dx.doi.org/10.2139/ssrn.3057570

Elie Benveniste

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

New York University
New York, NY 10012
United States

Gordon Ritter (Contact Author)

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

New York University
251 Mercer Street
New York, NY 10012
United States

City University of New York (CUNY) - Weissman School of Arts and Sciences ( email )

One Bernard Baruch Way
New York, NY 10010
United States

Columbia University - Department of Mathematics ( email )

New York, NY
United States

University of Chicago - Department of Mathematics ( email )

5734 S. University
Chicago, IL 60637
United States

Columbia University - School of Professional Studies ( email )

203 Lewisohn Hall
2970 Broadway, MC 4119
New York, NY 10027
United States

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