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Mathematics and Financial Economics

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01.09.2013

Utility maximization with a given pricing measure when the utility is not necessarily concave

verfasst von: Christian Reichlin

Erschienen in: Mathematics and Financial Economics | Ausgabe 4/2013

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Abstract

We study the problem of maximizing expected utility from terminal wealth for a not necessarily concave utility function \(U\) and for a budget set given by one fixed pricing measure. We prove the existence and several fundamental properties of a maximizer. We analyze the (not necessarily concave) value function (indirect utility) \(u(x,U)\). In particular, we show that the concave envelope of \(u(x,U)\) is the value function \(u(x,U_c)\) of the utility maximization problem for the concave envelope \(U_c\) of the utility function \(U\). The two value functions are shown to coincide if the underlying probability space is atomless. This allows us to characterize the maximizers for several model classes explicitly.

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Titel: Utility maximization with a given pricing measure when the utility is not necessarily concave
verfasst von: Christian Reichlin
Publikationsdatum: 01.09.2013
Verlag: Springer Berlin Heidelberg
Erschienen in: Mathematics and Financial Economics / Ausgabe 4/2013
Print ISSN: 1862-9679
Elektronische ISSN: 1862-9660
DOI: https://doi.org/10.1007/s11579-013-0093-x

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