Optimal Basket Liquidation for CARA Investors is Deterministic |
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Authors: | Alexander Schied Torsten Schöneborn Michael Tehranchi |
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Affiliation: | 1. Chair of Business Mathematics, Mannheim University , Mannheim, 68159, Germany schied@uni-mannheim.de;3. AHL Research, Man Investments Ltd., Sugar Quay , London, EC3R 6DU, UK;4. Statistical Laboratory , University of Cambridge , Cambridge, CB3 0WB, UK |
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Abstract: | 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, multiasset 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) Applied Mathematical Finance, 10, pp. 1–18], 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. |
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Keywords: | Market impact modelling illiquid markets optimal liquidation optimal trade execution algorithmic trading utility maximization Hamilton–Jacobi–Bellman equation finite fuel control |
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