A Unified Framework for Utility Maximization Problems: an Orlicz space approach

By Sara Biagini, Marco Frittelli. 2007

112 citations recorded by the source corpus.

We consider a stochastic financial incomplete market where the price processes are described by a vector valued semimartingale that is possibly non locally bounded. We face the classical problem of the utility maximization from terminal wealth, with utility functions that are finite valued over $(a,\infty )$, $a\in \lbrack -\infty ,\infty )$, and satisfy weak regularity assumptions. We adopt a class of trading strategies that allows for non locally bounded stochastic integrals. The embedding of the utility maximization problem in Orlicz spaces permits to formulate the problem in a unified way for both the cases: $a\in \mathbb{R}$ or $a=-\infty $. By duality methods we prove the existence of the optimal solutions to the primal and dual problems and show that a singular component in the pricing functionals may occur also with utility functions finite on the entire real line.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/a99fae9871095f6e34fb978a5623759a26815997

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In Economics and Econometrics

In Finance

In Management Science and Operations Research

Citations in the corpus

On the Extension of the Namioka-Klee Theorem and on the Fatou Property for Risk Measures (2009, background): “Moreover, in [BF08] it is shown that Orlicz spaces that can be associated with a utility function are the right framework for the utility maximization problems which commonly arises in nancial problems.”
MULTIVARIATE RISK MEASURES: A CONSTRUCTIVE APPROACH BASED ON SELECTIONS (2013, background): “The setting of Riesz spaces (partially ordered linear spaces), in particular Fréchet lattices and Orlicz spaces has become already common in the theory of risk measures, see [1, 4].”
INDIFFERENCE PRICE WITH GENERAL SEMIMARTINGALES (2009, methodology): “2 The Orlicz space framework This new framework for utility maximization was rst introduced by Biagini [B08] and then considerably expanded in [BF08], upon which this section is mostly based.”