IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1003.3582.html
   My bibliography  Save this paper

Risk Aversion Asymptotics for Power Utility Maximization

Author

Listed:
  • Marcel Nutz

Abstract

We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for general semimartingale models while the convergence of the optimal trading strategy is obtained for continuous models. The limits are related to exponential and logarithmic utility. To derive these results, we combine approaches from optimal control, convex analysis and backward stochastic differential equations (BSDEs).

Suggested Citation

  • Marcel Nutz, 2010. "Risk Aversion Asymptotics for Power Utility Maximization," Papers 1003.3582, arXiv.org.
    • Handle: RePEc:arx:papers:1003.3582
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1003.3582
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sara Biagini & Marco Frittelli, 2007. "The supermartingale property of the optimal wealth process for general semimartingales," Finance and Stochastics, Springer, vol. 11(2), pages 253-266, April.
    2. Sara Biagini & Marco Frittelli, 2005. "Utility maximization in incomplete markets for unbounded processes," Finance and Stochastics, Springer, vol. 9(4), pages 493-517, October.
    3. Yuri M. Kabanov & Christophe Stricker, 2002. "On the optimal portfolio for the exponential utility maximization: remarks to the six‐author paper," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 125-134, April.
    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. Markus Mocha & Nicholas Westray, 2011. "The Stability of the Constrained Utility Maximization Problem - A BSDE Approach," Papers 1107.0190, arXiv.org.
    2. Christoph Frei & Markus Mocha & Nicholas Westray, 2011. "BSDEs in Utility Maximization with BMO Market Price of Risk," Papers 1107.0183, arXiv.org, revised Feb 2012.

    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. Martin Herdegen & Johannes Muhle-Karbe, 2018. "Stability of Radner equilibria with respect to small frictions," Finance and Stochastics, Springer, vol. 22(2), pages 443-502, April.
    2. Xing, Hao, 2017. "Stability of the exponential utility maximization problem with respect to preferences," LSE Research Online Documents on Economics 57213, London School of Economics and Political Science, LSE Library.
    3. Westray, Nicholas & Zheng, Harry, 2009. "Constrained nonsmooth utility maximization without quadratic inf convolution," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1561-1579, May.
    4. Mark P. Owen & Gordan Žitković, 2009. "Optimal Investment With An Unbounded Random Endowment And Utility‐Based Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 129-159, January.
    5. M. Mania & R. Tevzadze, 2008. "Backward Stochastic PDEs related to the utility maximization problem," Papers 0806.0240, arXiv.org.
    6. Hao Xing, 2012. "Stability of the exponential utility maximization problem with respect to preferences," Papers 1205.6160, arXiv.org, revised Sep 2013.
    7. Mark Owen & Gordan Zitkovic, 2007. "Optimal Investment with an Unbounded Random Endowment and Utility-Based Pricing," Papers 0706.0478, arXiv.org, revised Sep 2007.
    8. Keita Owari, 2011. "On Admissible Strategies in Robust Utility Maximization," Papers 1109.5512, arXiv.org, revised Mar 2012.
    9. Johannes Gerer & Gregor Dorfleitner, 2016. "A Note On Utility Indifference Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-17, September.
    10. Huy N. Chau & Mikl'os R'asonyi, 2016. "Skorohod's representation theorem and optimal strategies for markets with frictions," Papers 1606.07311, arXiv.org, revised Apr 2017.
    11. Kallsen Jan & Rheinländer Thorsten, 2011. "Asymptotic utility-based pricing and hedging for exponential utility," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 17-36, March.
    12. Kim Weston, 2016. "Stability of utility maximization in nonequivalent markets," Finance and Stochastics, Springer, vol. 20(2), pages 511-541, April.
    13. Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
    14. Bruno Bouchard & Johannes Muhle-Karbe, 2022. "Simple Bounds for Transaction Costs," Post-Print hal-01711371, HAL.
    15. Gu, Lingqi & Lin, Yiqing & Yang, Junjian, 2016. "On the dual problem of utility maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1019-1035.
    16. Alessandro Doldi & Marco Frittelli, 2019. "Multivariate Systemic Optimal Risk Transfer Equilibrium," Papers 1912.12226, arXiv.org, revised Oct 2021.
    17. Tahir Choulli & Jun Deng & Junfeng Ma, 2012. "How Non-Arbitrage, Viability and Num\'eraire Portfolio are Related," Papers 1211.4598, arXiv.org, revised Jun 2014.
    18. Kim Weston, 2014. "Stability of Utility Maximization in Nonequivalent Markets," Papers 1410.0915, arXiv.org, revised Jun 2015.
    19. Miklos Rasonyi, 2015. "Maximizing expected utility in the Arbitrage Pricing Model," Papers 1508.07761, arXiv.org, revised Mar 2017.
    20. Bruno Bouchard & Johannes Muhle-Karbe, 2018. "Simple Bounds for Transaction Costs," Working Papers hal-01711371, HAL.

    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:1003.3582. 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.