Super-replication and utility maximization in large financial markets

Marzia De Donno, P. Guasoni and M. Pratelli

Stochastic Processes and their Applications, 2005, vol. 115, issue 12, 2006-2022

Abstract: We study the problems of super-replication and utility maximization from terminal wealth in a semimartingale model with countably many assets. After introducing a suitable definition of admissible strategy, we characterize superreplicable contingent claims in terms of martingale measures. Utility maximization problems are then studied with the convex duality method, and we extend finite-dimensional results to this setting. The existence of an optimizer is proved in a suitable class of generalized strategies: this class has also the property that maximal expected utility is the limit of maximal expected utilities in finite-dimensional submarkets. Finally, we illustrate our results with some examples in infinite dimensional factor models.

Keywords: Infinite-dimensional; stochastic; integration; Utility; maximization; Admissible; strategies; Convex; duality (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (17)

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