Optimal Execution with Uncertain Order Fills in Almgren-Chriss Framework
33 Pages Posted: 18 Jul 2015 Last revised: 17 Dec 2015
Date Written: July 17, 2015
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
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