Robust utility maximization with limited downside risk in incomplete markets |
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Authors: | Anne Gundel Stefan Weber |
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Institution: | 1. Humboldt-Universität, zu Berlin, Germany;2. School of Operations Research and Information Engineering, Cornell University, 279 Rhodes Hall, Ithaca, NY 14853, USA |
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Abstract: | In this article we consider the portfolio selection problem of an agent with robust preferences in the sense of Gilboa and Schmeidler Itzhak Gilboa, David Schmeidler, Maxmin expected utility with non-unique prior, Journal of Mathematical Economics 18 (1989) 141–153] in an incomplete market. Downside risk is constrained by a robust version of utility-based shortfall risk. We derive an explicit representation of the optimal terminal wealth in terms of certain worst case measures which can be characterized as minimizers of a dual problem. This dual problem involves a three-dimensional analogue of f-divergences which generalize the notion of relative entropy. |
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Keywords: | 91B16 91B28 62C 62P05 |
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