NDLI: Robust Utility Maximization without Model Compactness

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Fontbona, Joaquín Backhoff Veraguas, Julio D.
Copyright Year	2016
Abstract	We formulate conditions for the solvability of the problem of robust utility maximization from final wealth in continuous time financial markets, without assuming weak compactness of the densities of the uncertainty set, as customarily done in the literature. Relevant examples of such a situation typically arise when the uncertainty set is determined through moment constraints. Our approach is based on identifying functional spaces naturally associated with the elements of each problem. For general markets these are convex modular spaces, which we can use to prove a minimax equality and the existence of optimal strategies, by establishing and exploiting the compactness of the image through the utility function of the set of attainable wealths. In complete markets we additionally obtain the existence of a worst-case measure, and, combining our ideas with abstract entropy minimization techniques, we moreover provide a novel and general methodology to characterize it.
Sponsorship	Millenium Scientific Initiative Chile. Comisión Nacional de Investigación Científica y Tecnológica. Austrian Science Fund
Starting Page	70
Ending Page	103
Page Count	34
File Format	PDF
DOI	10.1137/140985718
e-ISSN	1945497X
Journal	SIAM Journal on Financial Mathematics (SJFMBJ)
Issue Number	1
Volume Number	7
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2016-03-03
Access Restriction	Subscribed
Subject Keyword	entropy minimization modular space Portfolio theory robust utility maximization noncompact uncertainty set Orlicz space Spaces of measurable functions Duality theory worst-case measure
Content Type	Text
Resource Type	Article

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