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Utility maximization in incomplete markets

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Author Info
Ying Hu
Peter Imkeller
Matthias Muller
Abstract

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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File URL: http://arxiv.org/abs/math/0508448
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number math/0508448.

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Date of creation: Aug 2005
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Publication status: Published in Annals of Applied Probability 2005, Vol. 15, No. 3, 1691-1712
Handle: RePEc:arx:papers:math/0508448

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  1. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272. [Downloadable!] (restricted)
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  1. Marie-Amelie Morlais, 2006. "Quadratic BSDEs driven by a continuous martingale and application to utility maximization problem," Quantitative Finance Papers math/0610749, arXiv.org, revised Mar 2008. [Downloadable!]
  2. Marie-Amelie Morlais, 2006. "Utility Maximization in a jump market model," Quantitative Finance Papers math/0612181, arXiv.org, revised May 2008. [Downloadable!]
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