Some Functional Analytic Tools for Utility Maximization

Alexander Gushchin, Ruslan V. Khasanov () and Ivan S. Morozov ()
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Ruslan V. Khasanov: Lomonosov Moscow State University
Ivan S. Morozov: Lomonosov Moscow State University

A chapter in Modern Stochastics and Applications, 2014, pp 267-285 from Springer

Abstract: Abstract The aim of the chapter is to extend the application of convex duality methods to the problem of maximizing expected utility from terminal wealth. More precisely, we restrict attention to a dual characterization of the value function of this problem and to a static setting. A general scheme to solve this problem is proposed. In the case where the utility function is finite on $$\mathbb{R}$$ , we use the approach, suggested by Biagini and Frittelli, based on using an Orlicz space constructed from an investor’s utility function. We reduce the original problem to an optimization problem in this space in a nontrivial way, which allows us to weaken essentially assumptions on the model. We also study the problem of utility maximization with random endowment considered by Cvitanić, Schachermayer, and Wang. Using the space ψ L ∞ with a weight function ψ constructed from a random endowment permits us to consider unbounded random endowments. Another important contribution is that in both problems under consideration, we provide versions of the dual problem that are free of singular functionals.

Keywords: Dual Problem; Banach Lattice; Orlicz Space; Young Function; Terminal Wealth (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-03512-3_15

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DOI: 10.1007/978-3-319-03512-3_15

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