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May 2004 Dual formulation of the utility maximization problem: The case of nonsmooth utility
B. Bouchard, N. Touzi, A. Zeghal
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Ann. Appl. Probab. 14(2): 678-717 (May 2004). DOI: 10.1214/105051604000000062

Abstract

We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results in this literature in two directions. First, we allow for nonsmooth utility functions, so as to include the shortfall minimization problems in our framework. Second, we allow for the presence of some given liability or a random endowment. In particular, these results provide a dual formulation of the utility indifference valuation rule.

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B. Bouchard. N. Touzi. A. Zeghal. "Dual formulation of the utility maximization problem: The case of nonsmooth utility." Ann. Appl. Probab. 14 (2) 678 - 717, May 2004. https://doi.org/10.1214/105051604000000062

Information

Published: May 2004
First available in Project Euclid: 23 April 2004

zbMATH: 1126.91018
MathSciNet: MR2052898
Digital Object Identifier: 10.1214/105051604000000062

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

Keywords: convex duality , incomplete markets , utility maximization

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.14 • No. 2 • May 2004
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