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August 2005 Utility maximization in incomplete markets
Ying Hu, Peter Imkeller, Matthias Müller
Ann. Appl. Probab. 15(3): 1691-1712 (August 2005). DOI: 10.1214/105051605000000188


We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors’ trading strategies we allow underly constraints described by closed, but not necessarily convex, sets. The final wealths obtained by trading under these constraints are identified as stochastic processes which usually are supermartingales, and even martingales for particular strategies. These strategies are seen to be optimal, and the corresponding value functions determined simply by the initial values of the supermartingales. We separately treat the cases of exponential, power and logarithmic utility.


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Ying Hu. Peter Imkeller. Matthias Müller. "Utility maximization in incomplete markets." Ann. Appl. Probab. 15 (3) 1691 - 1712, August 2005.


Published: August 2005
First available in Project Euclid: 15 July 2005

zbMATH: 1083.60048
MathSciNet: MR2152241
Digital Object Identifier: 10.1214/105051605000000188

Primary: 60H10, 91B28
Secondary: 60G44, 60H20, 91B16, 91B70, 93E20

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.15 • No. 3 • August 2005
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