Optimal Basket Liquidation for CARA Investors is Deterministic

19 Pages Posted: 6 Nov 2009 Last revised: 24 Feb 2010

Alexander Schied

University of Mannheim

Torsten Schoeneborn

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

Michael Tehranchi

University of Cambridge

Date Written: 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.

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

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

Suggested Citation

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

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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