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.
De Donno, M., P., G., M., P., Super-replication and utility maximization in large financial markets, <<STOCHASTIC PROCESSES AND THEIR APPLICATIONS>>, 2005; 115 (12): 2006-2022. [doi:10.1016/j.spa.2005.06.010] [http://hdl.handle.net/10807/168912]
Super-replication and utility maximization in large financial markets
De Donno, Marzia;
2005
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.
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