Open Access
April 2013 On utility maximization under convex portfolio constraints
Kasper Larsen, Gordan Žitković
Ann. Appl. Probab. 23(2): 665-692 (April 2013). DOI: 10.1214/12-AAP850


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.


Download Citation

Kasper Larsen. Gordan Žitković. "On utility maximization under convex portfolio constraints." Ann. Appl. Probab. 23 (2) 665 - 692, April 2013.


Published: April 2013
First available in Project Euclid: 12 February 2013

zbMATH: 1262.91129
MathSciNet: MR3059272
Digital Object Identifier: 10.1214/12-AAP850

Primary: 91G10 , 91G80

Keywords: convex constraints , convex duality , finitely-additive measures , Semimartingales , utility maximization

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.23 • No. 2 • April 2013
Back to Top