IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb649/sfb649dp2007-026.html
   My bibliography  Save this paper

Robust optimal control for a consumption-investment problem

Author

Listed:
  • Schied, Alexander

Abstract

We give an explicit PDE characterization for the solution of the problem of maximizing the utility of both terminal wealth and intertemporal consumption under model uncertainty. The underlying market model consists of a risky asset, whose volatility and long-term trend are driven by an external stochastic factor process. The robust utility functional is defined in terms of a HARA utility function with risk aversion parameter 0

Suggested Citation

  • Schied, Alexander, 2007. "Robust optimal control for a consumption-investment problem," SFB 649 Discussion Papers 2007-026, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2007-026
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/25198/1/558547737.PDF
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Schied, Alexander, 2005. "Optimal investments for risk- and ambiguity-averse preferences: A duality approach," SFB 649 Discussion Papers 2005-051, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. Anne Gundel, 2005. "Robust utility maximization for complete and incomplete market models," Finance and Stochastics, Springer, vol. 9(2), pages 151-176, April.
    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. Schied, Alexander & Wu, Ching-Tang, 2005. "Duality theory for optimal investments under model uncertainty," SFB 649 Discussion Papers 2005-025, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Denis Talay & Ziyu Zheng, 2002. "Worst case model risk management," Finance and Stochastics, Springer, vol. 6(4), pages 517-537.
    9. Hernández-Hernández, Daniel & Schied, Alexander, 2006. "A control approach to robust utility maximization with logarithmic utility and time-consistent penalties," SFB 649 Discussion Papers 2006-061, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    10. Hernández-Hernández, Daniel & Schied, Alexander, 2005. "Robust utility maximization in a stochastic factor model," SFB 649 Discussion Papers 2006-007, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    11. Burgert Christian & Rüschendorf Ludger, 2005. "Optimal consumption strategies under model uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 1-14, January.
    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. repec:hum:wpaper:sfb649dp2007-060 is not listed on IDEAS
    2. Thomas Knispel, 2012. "Asymptotics of robust utility maximization," Papers 1203.1191, arXiv.org.
    3. Perederiy, Volodymyr, 2007. "Kombinierte Liquiditäts- und Solvenzkennzahlen und ein darauf basierendes Insolvenzprognosemodell für deutsche GmbHs," SFB 649 Discussion Papers 2007-060, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.

    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:sfb649dp2007-026 is not listed on IDEAS
    2. repec:hum:wpaper:sfb649dp2006-061 is not listed on IDEAS
    3. Hernández-Hernández, Daniel & Schied, Alexander, 2006. "A control approach to robust utility maximization with logarithmic utility and time-consistent penalties," SFB 649 Discussion Papers 2006-061, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. Sigrid Kallblad, 2013. "Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals," Papers 1311.7419, arXiv.org.
    5. Thomas Knispel, 2012. "Asymptotics of robust utility maximization," Papers 1203.1191, arXiv.org.
    6. Hernández-Hernández, Daniel & Schied, Alexander, 2007. "Robust maximization of consumption with logarithmic utility," SFB 649 Discussion Papers 2007-030, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. repec:hum:wpaper:sfb649dp2007-030 is not listed on IDEAS
    8. repec:hum:wpaper:sfb649dp2006-007 is not listed on IDEAS
    9. repec:hum:wpaper:sfb649dp2006-063 is not listed on IDEAS
    10. 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.
    11. Wittmüß, Wiebke, 2006. "Robust optimization of consumption with random endowment," SFB 649 Discussion Papers 2006-063, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    12. Hernández-Hernández, Daniel & Schied, Alexander, 2005. "Robust utility maximization in a stochastic factor model," SFB 649 Discussion Papers 2006-007, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. 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.
    14. 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.
    15. 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.
    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:sfb649dp2005-051 is not listed on IDEAS
    18. Owari, Keita & 尾張, 圭太, 2008. "Robust Exponential Hedging and Indifference Valuation," Discussion Papers 2008-09, Graduate School of Economics, Hitotsubashi University.
    19. Schied, Alexander, 2005. "Optimal investments for risk- and ambiguity-averse preferences: A duality approach," SFB 649 Discussion Papers 2005-051, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    20. Kardaras, Constantinos & Robertson, Scott, 2012. "Robust maximization of asymptotic growth," LSE Research Online Documents on Economics 44994, London School of Economics and Political Science, LSE Library.
    21. 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.
    22. 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.
    23. Keita Owari, 2011. "On Admissible Strategies in Robust Utility Maximization," Papers 1109.5512, arXiv.org, revised Mar 2012.
    24. 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.
    25. Bogdan Iftimie, 2023. "A robust investment-consumption optimization problem in a switching regime interest rate setting," Journal of Global Optimization, Springer, vol. 86(3), pages 713-739, July.
    26. Keita Owari, 2011. "ON ADMISSIBLE STRATEGIES IN ROBUST UTILITY MAXIMIZATION(Revised in March 2012, Forthcoming in "Mathematics and Financial Economics")," CARF F-Series CARF-F-257, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

    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:zbw:sfb649:sfb649dp2007-026. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sohubde.html .

    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.