IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1203.1191.html

Asymptotics of robust utility maximization

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1203.1191
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:hum:wpaper:sfb649dp2006-007 is not listed on IDEAS
    2. Alexander Schied, 2008. "Robust optimal control for a consumption-investment problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 1-20, February.
    3. 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.
    4. Alexander Schied, 2005. "Optimal Investments for Robust Utility Functionals in Complete Market Models," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 750-764, August.
    5. Schied Alexander & Wu Ching-Tang, 2005. "Duality theory for optimal investments under model uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 23(3), pages 199-217, March.
    6. Hernández-Hernández Daniel & Schied Alexander, 2006. "Robust utility maximization in a stochastic factor model," Statistics & Risk Modeling, De Gruyter, vol. 24(1), pages 109-125, July.
    7. 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, April.
    8. repec:hum:wpaper:sfb649dp2005-025 is not listed on IDEAS
    9. repec:hum:wpaper:sfb649dp2007-026 is not listed on IDEAS
    10. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Huy N. Chau & Miklos Rasonyi, 2018. "Robust utility maximization in markets with transaction costs," Papers 1803.04213, arXiv.org, revised Dec 2018.
    2. Huy N. Chau & Miklós Rásonyi, 2019. "Robust utility maximisation in markets with transaction costs," Finance and Stochastics, Springer, vol. 23(3), pages 677-696, July.
    3. 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.
    4. Juan Li & Wenqiang Li & Gechun Liang, 2020. "A game theoretical approach to homothetic robust forward investment performance processes in stochastic factor models," Papers 2005.10660, arXiv.org, revised May 2021.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:hum:wpaper:sfb649dp2006-061 is not listed on IDEAS
    2. Keita Owari, 2013. "A Robust Version of Convex Integral Functionals," Papers 1305.6023, arXiv.org, revised May 2015.
    3. repec:hum:wpaper:sfb649dp2007-030 is not listed on IDEAS
    4. repec:hum:wpaper:sfb649dp2007-026 is not listed on IDEAS
    5. Keita Owari, 2013. "A Robust Version of Convex Integral Functionals," CARF F-Series CARF-F-319, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Alexander Schied, 2007. "Optimal investments for risk- and ambiguity-averse preferences: a duality approach," Finance and Stochastics, Springer, vol. 11(1), pages 107-129, January.
    7. Sigrid Kallblad, 2013. "Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals," Papers 1311.7419, arXiv.org.
    8. Sigrid Kallblad & Jan Obloj & Thaleia Zariphopoulou, 2013. "Time--consistent investment under model uncertainty: the robust forward criteria," Papers 1311.3529, arXiv.org, revised Nov 2014.
    9. Qian Lin & Frank Riedel, 2021. "Optimal consumption and portfolio choice with ambiguous interest rates and volatility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1189-1202, April.
    10. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
    11. Belkacem Berdjane & Sergei Pergamenshchikov, 2012. "Sequential $\delta$-optimal consumption and investment for stochastic volatility markets with unknown parameters," Working Papers hal-00743164, HAL.
    12. Daniel Hern'andez-Hern'andez & Leonel P'erez-Hern'andez, 2012. "Robust utility maximization for L\'evy processes: Penalization and solvability," Papers 1206.0715, arXiv.org.
    13. Juan Li & Wenqiang Li & Gechun Liang, 2020. "A game theoretical approach to homothetic robust forward investment performance processes in stochastic factor models," Papers 2005.10660, arXiv.org, revised May 2021.
    14. Guohui Guan & Zongxia Liang & Yilun Song, 2022. "The continuous-time pre-commitment KMM problem in incomplete markets," Papers 2210.13833, arXiv.org, revised Feb 2023.
    15. 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.
    16. Gundel, Anne & Weber, Stefan, 2008. "Utility maximization under a shortfall risk constraint," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1126-1151, December.
    17. repec:hum:wpaper:sfb649dp2006-007 is not listed on IDEAS
    18. repec:hum:wpaper:sfb649dp2006-063 is not listed on IDEAS
    19. Wing Fung Chong & Gechun Liang, 2018. "Optimal investment and consumption with forward preferences and uncertain parameters," Papers 1807.01186, arXiv.org, revised Nov 2023.
    20. repec:hum:wpaper:sfb649dp2005-051 is not listed on IDEAS
    21. Hiroaki Hata, 2021. "Risk-Sensitive Asset Management with Lognormal Interest Rates," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 28(2), pages 169-206, June.
    22. Tadashi Hayashi & Jun Sekine, 2011. "Risk-sensitive Portfolio Optimization with Two-factor Having a Memory Effect," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(4), pages 385-403, November.
    23. Sigrid Källblad & Jan Obłój & Thaleia Zariphopoulou, 2018. "Dynamically consistent investment under model uncertainty: the robust forward criteria," Finance and Stochastics, Springer, vol. 22(4), pages 879-918, October.
    24. Frank Thomas Seifried, 2010. "Optimal Investment for Worst-Case Crash Scenarios: A Martingale Approach," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 559-579, August.
    25. Ariel Neufeld & Julian Sester, 2024. "Non-concave stochastic optimal control in finite discrete time under model uncertainty," Papers 2404.05230, arXiv.org, revised May 2025.
    26. Tim Leung & Qingshuo Song & Jie Yang, 2013. "Outperformance portfolio optimization via the equivalence of pure and randomized hypothesis testing," Finance and Stochastics, Springer, vol. 17(4), pages 839-870, October.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1203.1191. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.