Abstract.
We investigate the problem of maximizing the robust utility functional \(\inf_{Q \in \mathcal{Q}} E_Qu(X)\). We give the dual characterization for its solution for both a complete and an incomplete market model. To this end, we introduce the new notion of reverse f-projections and use techniques developed for f-divergences. This is a suitable tool to reduce the robust problem to the classical problem of utility maximization under a certain measure: the reverse f-projection. Furthermore, we give the dual characterization for a closely related problem, the minimization of expenditures given a minimum level of expected utility in a robust setting and for an incomplete market.
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Received: September 2004,
Mathematics Subject Classification (2000):
62C20, 62O05, 91B16, 91B28
JEL Classification:
D81, G11
I thank Hans Föllmer for his help when writing this paper. Furthermore, I thank Alexander Schied for discussing the topic with me and Michael Kupper and the referees for their helpful remarks.
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Gundel, A. Robust utility maximization for complete and incomplete market models. Finance Stochast. 9, 151–176 (2005). https://doi.org/10.1007/s00780-004-0148-1
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DOI: https://doi.org/10.1007/s00780-004-0148-1