A unified framework for utility maximization problems: An Orlicz space approach

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dc.creatorBiagini, Sara
dc.creatorFrittelli, Marco
dc.date2008-06-16
dc.date.accessioned2026-07-07T12:19:33Z
dc.date.available2026-07-07T12:19:33Z
dc.descriptionWe consider a stochastic financial incomplete market where the price processes are described by a vector-valued semimartingale that is possibly nonlocally bounded. We face the classical problem of 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 stochastic integrals that are not necessarily bounded from below. The embedding of the utility maximization problem in Orlicz spaces permits us to formulate the problem in a unified way for both the cases $a\in\mathbb{R}$ and $a=-\infty$. By duality methods, we prove the existence of solutions to the primal and dual problems and show that a singular component in the pricing functionals may also occur with utility functions finite on the entire real line.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AAP469 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0806.2582
dc.identifierhttp://arxiv.org/abs/0806.2582
dc.identifierAnnals of Applied Probability 2008, Vol. 18, No. 3, 929-966
dc.identifierdoi:10.1214/07-AAP469
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212791
dc.subjectProbability
dc.subject60G48, 60G44, 49N15, 91B28 (Primary) 46E30, 46N30, 91B16 (Secondary)
dc.titleA unified framework for utility maximization problems: An Orlicz space approach
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