The Annals of Applied Probability

On utility maximization under convex portfolio constraints

Abstract

We consider a utility-maximization problem in a general semimartingale financial model, subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose values do not necessarily contain the origin; that is, it may be inadmissible for an investor to hold no risky investment at all. Such a setup subsumes the classical constrained utility-maximization problem, as well as the problem where illiquid assets or a random endowment are present.

Our main result establishes the existence of optimal trading strategies in such models under no smoothness requirements on the utility function. The result also shows that, up to attainment, the dual optimization problem can be posed over a set of countably-additive probability measures, thus eschewing the need for the usual finitely-additive enlargement.

Article information

Source
Ann. Appl. Probab., Volume 23, Number 2 (2013), 665-692.

Dates
First available in Project Euclid: 12 February 2013

https://projecteuclid.org/euclid.aoap/1360682026

Digital Object Identifier
doi:10.1214/12-AAP850

Mathematical Reviews number (MathSciNet)
MR3059272

Zentralblatt MATH identifier
1262.91129

Citation

Larsen, Kasper; Žitković, Gordan. On utility maximization under convex portfolio constraints. Ann. Appl. Probab. 23 (2013), no. 2, 665--692. doi:10.1214/12-AAP850. https://projecteuclid.org/euclid.aoap/1360682026

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