Optimal Execution with Uncertain Order Fills in Almgren-Chriss Framework

33 Pages Posted: 18 Jul 2015 Last revised: 17 Dec 2015

See all articles by Xue Cheng

Xue Cheng

Peking University - School of Mathematical Sciences

Marina Di Giacinto

University of Cassino

Tai-Ho Wang

Baruch College, CUNY

Date Written: July 17, 2015

Abstract

The classical price impact model of Almgren and Chriss is extended to incorporate the uncertainty of order fills. The extended model can be recast as alternatives to uncertain impact models and stochastic liquidity models. Optimal strategies are determined by maximizing the expected final P&L and various P&L-risk tradeoffs including utility maximization. Closed form expressions for optimal strategies are obtained in linear cases. The results suggest a type of adaptive VWAP, adaptive POV and adaptive Almgren-Chriss strategies. VWAP and classical Almgren-Chriss strategies are recovered as limiting cases with different characteristic time scale of liquidation for the latter.

Keywords: Hamilton-Jacobi-Bellman equation, optimal execution, order fill uncertainty, price impact, stochastic control, utility maximization

Suggested Citation

Cheng, Xue and Di Giacinto, Marina and Wang, Tai-Ho, Optimal Execution with Uncertain Order Fills in Almgren-Chriss Framework (July 17, 2015). Available at SSRN: https://ssrn.com/abstract=2632012 or http://dx.doi.org/10.2139/ssrn.2632012

Xue Cheng (Contact Author)

Peking University - School of Mathematical Sciences ( email )

Peking
China

Marina Di Giacinto

University of Cassino ( email )

Via S. Angelo, Loc. Folcara
Cassino, Frosinone 03043
Italy

Tai-Ho Wang

Baruch College, CUNY ( email )

1 Bernard Baruch Way
New York, NY 10010
United States
+1-646-312-4130 (Phone)

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