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Constrained NonSmooth Utility Maximization on the Positive Real Line

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  • Nicholas Westray
  • Harry Zheng

Abstract

We maximize the expected utility of terminal wealth in an incomplete market where there are cone constraints on the investor's portfolio process and the utility function is not assumed to be strictly concave or differentiable. We establish the existence of the optimal solutions to the primal and dual problems and their dual relationship. We simplify the present proofs in this area and extend the existing duality theory to the constrained nonsmooth setting.

Suggested Citation

  • Nicholas Westray & Harry Zheng, 2010. "Constrained NonSmooth Utility Maximization on the Positive Real Line," Papers 1010.4055, arXiv.org.
    • Handle: RePEc:arx:papers:1010.4055
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    References listed on IDEAS

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    1. B. Bouchard & N. Touzi & A. Zeghal, 2004. "Dual formulation of the utility maximization problem: the case of nonsmooth utility," Papers math/0405290, arXiv.org.
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    8. Westray, Nicholas & Zheng, Harry, 2009. "Constrained nonsmooth utility maximization without quadratic inf convolution," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1561-1579, May.
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