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Asymptotics of robust utility maximization

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  • Thomas Knispel
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    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.

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    File URL: http://arxiv.org/pdf/1203.1191
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1203.1191.

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    Date of creation: Mar 2012
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    Publication status: Published in Annals of Applied Probability 2012, Vol. 22, No. 1, 172-212
    Handle: RePEc:arx:papers:1203.1191

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    Web page: http://arxiv.org/

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