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

Zhegal, Amina; Touzi, Nizar; Bouchard, Bruno

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

Number

Publisher

Institute of Mathematical Statistics

Pages

678-717

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