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November 2001 Dual Formulation of the Utility Maximization Problem Under Transaction Costs
Griselda Deelstra, Huyên Pham, Nizar Touzi
Ann. Appl. Probab. 11(4): 1353-1383 (November 2001). DOI: 10.1214/aoap/1015345406


In the context of a general multivariate financial market with transaction costs, we consider the problem of maximizing expected utility from terminal wealth. In contrast with the existing literature, where only the liquidation value of the terminal portfolio is relevant, we consider general utility functions which are only required to be consistent with the structure of the transaction costs. An important feature of our analysis is that the utility function is not required to be $C^1$. Such nonsmoothness is suggested by major natural examples. Our main result is an extension of the well-known dual formulation of the utility maximization problem to this context.


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Griselda Deelstra. Huyên Pham. Nizar Touzi. "Dual Formulation of the Utility Maximization Problem Under Transaction Costs." Ann. Appl. Probab. 11 (4) 1353 - 1383, November 2001.


Published: November 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1012.60059
MathSciNet: MR1878301
Digital Object Identifier: 10.1214/aoap/1015345406

Primary: 49J52 , 90A09 , 93E20
Secondary: 60H30 , 90A16

Keywords: dual formulation , nonsmooth analysis , Transaction costs , utility maximization

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.11 • No. 4 • November 2001
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