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
TypeArticle accepté pour publication ou publié
External document linkhttp://projecteuclid.org/euclid.aoap/1082737107
Journal nameThe Annals of Applied Probability
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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 / Keywordsconvex duality; incomplete markets; Utility maximization
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