Super-replication and utility maximization in large financial markets

Marzia De Donno, P. Guasoni, M. Pratelli

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

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 sub-markets. Finally, we illustrate our results with some examples in infinite dimensional factor models.
Original languageEnglish
Pages (from-to)2006-2022
Number of pages17
JournalStochastic Processes and their Applications
Volume115
DOIs
Publication statusPublished - 2005

Keywords

  • infinite-dimensional stochastic integration, utility maximization, admissible strategies, convex duality

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