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Constrained Nonsmooth Utility Maximization On The Positive Real Line

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Executive Summary

The authors 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. They establish the existence of the optimal solutions to the primal and dual problems and their dual relationship. They simplify the present proofs in this area and extend the existing duality theory to the constrained nonsmooth setting. Utility maximization is a classical theme in mathematical finance and there is already a substantial body of literature devoted to the study of the problem in both complete and incomplete semimartingale models.

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