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Asymptotics of robust utility maximization

Author

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• Thomas Knispel

Abstract

For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\lambda\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.

Suggested Citation

• Thomas Knispel, 2012. "Asymptotics of robust utility maximization," Papers 1203.1191, arXiv.org.
• Handle: RePEc:arx:papers:1203.1191
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File URL: http://arxiv.org/pdf/1203.1191

References listed on IDEAS

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1. Schied Alexander & Wu Ching-Tang, 2005. "Duality theory for optimal investments under model uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 23(3/2005), pages 199-217, March.
2. W. H. Fleming & S. J. Sheu, 2000. "Risk-Sensitive Control and an Optimal Investment Model," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 197-213.
3. Daniel Hernandez–Hernandez & Alexander Schied, 2005. "Robust Utility Maximization in a Stochastic Factor Model," SFB 649 Discussion Papers SFB649DP2006-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2006.
4. Alexander Schied & Ching-Tang Wu, 2005. "Duality theory for optimal investments under model uncertainty," SFB 649 Discussion Papers SFB649DP2005-025, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Sep 2005.
5. Alexander Schied, 2007. "Robust Optimal Control for a Consumption-investment Problem," SFB 649 Discussion Papers SFB649DP2007-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
6. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
7. Hernández-Hernández Daniel & Schied Alexander, 2006. "Robust utility maximization in a stochastic factor model," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-17, July.
8. Hiroaki Hata & Yasunari Iida, 2006. "A risk-sensitive stochastic control approach to an optimal investment problem with partial information," Finance and Stochastics, Springer, vol. 10(3), pages 395-426, September.
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Cited by:

1. Oleksii Mostovyi, 2015. "Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption," Finance and Stochastics, Springer, vol. 19(1), pages 135-159, January.

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