Optimal Trade Execution under Geometric Brownian Motion in the Almgren and Chriss Framework

14 Pages Posted: 6 Aug 2010 Last revised: 3 Oct 2012

See all articles by Jim Gatheral

Jim Gatheral

CUNY Baruch College

Alexander Schied

University of Mannheim

Date Written: October 2, 2012

Abstract

With an alternative choice of risk criterion, we solve the HJB equation explicitly to find a closed-form solution for the optimal trade execution strategy in the Almgren-Chriss framework assuming the underlying unaffected stock price process is geometric Brownian motion.

Keywords: HJB, optimal execution, risk measures, market impact

Suggested Citation

Gatheral, Jim and Schied, Alexander, Optimal Trade Execution under Geometric Brownian Motion in the Almgren and Chriss Framework (October 2, 2012). International Journal of Theoretical and Applied Finance, Vol. 14, No. 3, pp. 353-368, 2011. Available at SSRN: https://ssrn.com/abstract=1654151

Jim Gatheral (Contact Author)

CUNY Baruch College ( email )

Department of Mathematics
One Bernard Baruch Way
New York, NY 10010
United States

Alexander Schied

University of Mannheim ( email )

Department of Mathematics
A 5, 6
Mannheim, 68131
Germany
+49-621-181-2513 (Phone)

HOME PAGE: http://www.alexschied.de/

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