# Robust utility maximization for complete and incomplete market models

## Author Info

• Anne Gundel

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## 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. Copyright Springer-Verlag Berlin/Heidelberg 2005

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## Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 9 (2005)
Issue (Month): 2 (04)
Pages: 151-176

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Handle: RePEc:spr:finsto:v:9:y:2005:i:2:p:151-176

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## Related research

Keywords: f-divergences; utility maximization; robust utility functionals; model uncertainty; incomplete markets; duality;

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## Citations

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Cited by:
1. Stefan Ankirchner, 2005. "Utility duality under additional information: conditional measures versus filtration enlargements," SFB 649 Discussion Papers SFB649DP2005-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
2. Gundel, Anne & Weber, Stefan, 2008. "Utility maximization under a shortfall risk constraint," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1126-1151, December.
3. Revaz Tevzadze & Teimuraz Toronjadze & Tamaz Uzunashvili, 2013. "Robust utility maximization for a diffusion market model with misspecified coefficients," Finance and Stochastics, Springer, vol. 17(3), pages 535-563, July.
4. Constantinos Kardaras & Scott Robertson, 2012. "Robust maximization of asymptotic growth," LSE Research Online Documents on Economics 44994, London School of Economics and Political Science, LSE Library.
5. A. Hoseinzadeh & G. Mohtashami Borzadaran & G. Yari, 2012. "Aspects concerning entropy and utility," Theory and Decision, Springer, vol. 72(2), pages 273-285, February.
6. Grzegorz Hara\'nczyk & Wojciech S{\l}omczy\'nski & Tomasz Zastawniak, 2007. "Relative and Discrete Utility Maximising Entropy," Papers 0709.1281, arXiv.org.
7. Wiebke Wittmüß, 2006. "Robust Optimization of Consumption with Random Endowment," SFB 649 Discussion Papers SFB649DP2006-063, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
8. Alexander Schied, 2007. "Robust Optimal Control for a Consumption-investment Problem," SFB 649 Discussion Papers SFB649DP2007-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
9. Xiaoxian Ma & Qingzhen Zhao & Jilin Qu, 2008. "Robust portfolio optimization with a generalized expected utility model under ambiguity," Annals of Finance, Springer, vol. 4(4), pages 431-444, October.
10. Constantinos Kardaras & Scott Robertson, 2010. "Robust maximization of asymptotic growth," Papers 1005.3454, arXiv.org, revised Aug 2012.
11. Alexander Schied, 2008. "Robust optimal control for a consumption-investment problem," Computational Statistics, Springer, vol. 67(1), pages 1-20, February.

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