Abstract

http://ssrn.com/abstract=1500277
 
 

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Optimal Basket Liquidation for CARA Investors is Deterministic


Alexander Schied


University of Mannheim

Torsten Schoeneborn


AHL (Man Investments); University of Oxford - Oxford-Man Institute of Quantitative Finance

Michael Tehranchi


University of Cambridge

February 23, 2010


Abstract:     
We consider the problem faced by an investor who must liquidate a given basket of assets over a finite time horizon. The investor’s goal is to maximize the expected utility of the sales revenues over a class of adaptive strategies. We assume that the investor’s utility has constant absolute risk aversion (CARA) and that the asset prices are given by a very general continuous-time, multi-asset price impact model. Our main result is that (perhaps surprisingly) the investor does no worse if he narrows his search to deterministic strategies. In the case where the asset prices are given by an extension of the nonlinear price impact model of Almgren (2003), we characterize the unique optimal strategy via the solution of a Hamilton equation and the value function via a nonlinear partial differential equation with singular initial condition.

Number of Pages in PDF File: 19

Keywords: Liquidity, illiquid markets, optimal liquidation strategies, dynamic trading strategies, algorithmic trading, utility maximization

JEL Classification: G10, G12, G20, G24, G33

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Date posted: November 6, 2009 ; Last revised: February 24, 2010

Suggested Citation

Schied, Alexander and Schoeneborn, Torsten and Tehranchi, Michael, Optimal Basket Liquidation for CARA Investors is Deterministic (February 23, 2010). Available at SSRN: http://ssrn.com/abstract=1500277 or http://dx.doi.org/10.2139/ssrn.1500277

Contact Information

Alexander Schied (Contact Author)
University of Mannheim ( email )
Department of Mathematics
A 5, 6
Mannheim, 68131
Germany
+49-621-181-2513 (Phone)
HOME PAGE: http://www.alexschied.de/
Torsten Schoeneborn
AHL (Man Investments) ( email )
Sugar Quay
Lower Thames Street
London, EC3R 6DU
Great Britain
University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )
Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom
Michael Tehranchi
University of Cambridge ( email )
Centre for Mathematical Sciences
Cambridge, CB3 0WB
United Kingdom
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