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Dual Formulation of the Utility Maximization Problem : the case of Nonsmooth Utility

Zhegal, Amina; Touzi, Nizar; Bouchard, Bruno (2004), Dual Formulation of the Utility Maximization Problem : the case of Nonsmooth Utility, The Annals of Applied Probability, 14, 2, p. 678-717. http://dx.doi.org/10.1214/105051604000000062

Type
Article accepté pour publication ou publié
External document link
http://projecteuclid.org/euclid.aoap/1082737107
Date
2004
Journal name
The Annals of Applied Probability
Volume
14
Number
2
Publisher
Institute of Mathematical Statistics
Pages
678-717
Publication identifier
http://dx.doi.org/10.1214/105051604000000062
Metadata
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Author(s)
Zhegal, Amina
Touzi, Nizar
Bouchard, Bruno
Abstract (EN)
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.
Subjects / Keywords
convex duality; incomplete markets; Utility maximization
JEL
D52 - Incomplete Markets

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