IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i5p1561-1579.html
   My bibliography  Save this article

Constrained nonsmooth utility maximization without quadratic inf convolution

Author

Listed:
  • Westray, Nicholas
  • Zheng, Harry

Abstract

We address a constrained utility maximization problem in an incomplete market for a utility function defined on the whole real line. We extend current research in two directions, firstly we allow for constraints on the portfolio process. Secondly we prove our results without relying on the technique of quadratic inf convolution, simplifying the proofs in this area.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:5:p:1561-1579
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(08)00125-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. B. Bouchard & N. Touzi & A. Zeghal, 2004. "Dual formulation of the utility maximization problem: the case of nonsmooth utility," Papers math/0405290, arXiv.org.
    2. Griselda Deelstra & Huyên Pham & Nizar Touzi, 2001. "Dual formulation of the utility maximisation problem under transaction costs," ULB Institutional Repository 2013/7596, ULB -- Universite Libre de Bruxelles.
    3. repec:dau:papers:123456789/1531 is not listed on IDEAS
    4. repec:dau:papers:123456789/1532 is not listed on IDEAS
    5. Sara Biagini & Marco Frittelli, 2005. "Utility maximization in incomplete markets for unbounded processes," Finance and Stochastics, Springer, vol. 9(4), pages 493-517, October.
    6. Frank Oertel & Mark Owen, 2006. "On utility-based super-replication prices of contingent claims with unbounded payoffs," Papers math/0609403, arXiv.org.
    7. 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.
    8. Bruno Bouchard, 2002. "Utility maximization on the real line under proportional transaction costs," Finance and Stochastics, Springer, vol. 6(4), pages 495-516.
    9. Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    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. Frank Seifried, 2010. "Optimal investment with deferred capital gains taxes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 181-199, February.
    2. Nicholas Westray & Harry Zheng, 2010. "Constrained NonSmooth Utility Maximization on the Positive Real Line," Papers 1010.4055, arXiv.org.
    3. Shaolin Ji & Xiaomin Shi, 2016. "Recursive utility optimization with concave coefficients," Papers 1607.00721, arXiv.org.
    4. Maxim Bichuch & Stephan Sturm, 2011. "Portfolio Optimization under Convex Incentive Schemes," Papers 1109.2945, arXiv.org, revised Oct 2013.
    5. Maxim Bichuch & Stephan Sturm, 2014. "Portfolio optimization under convex incentive schemes," Finance and Stochastics, Springer, vol. 18(4), pages 873-915, October.

    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. Nicholas Westray & Harry Zheng, 2010. "Constrained NonSmooth Utility Maximization on the Positive Real Line," Papers 1010.4055, arXiv.org.
    2. Nicholas Westray & Harry Zheng, 2011. "Minimal sufficient conditions for a primal optimizer in nonsmooth utility maximization," Finance and Stochastics, Springer, vol. 15(3), pages 501-512, September.
    3. 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.
    4. Miklos Rasonyi, 2017. "On utility maximization without passing by the dual problem," Papers 1702.00982, arXiv.org, revised Mar 2018.
    5. Yiqing Lin & Junjian Yang, 2016. "Utility maximization problem with random endowment and transaction costs: when wealth may become negative," Papers 1604.08224, arXiv.org, revised Sep 2016.
    6. Czichowsky, Christoph & Schachermayer, Walter & Yang, Junjian, 2017. "Shadow prices for continuous processes," LSE Research Online Documents on Economics 63370, London School of Economics and Political Science, LSE Library.
    7. 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.
    8. Alessandro Doldi & Marco Frittelli, 2019. "Multivariate Systemic Optimal Risk Transfer Equilibrium," Papers 1912.12226, arXiv.org, revised Oct 2021.
    9. Dumas, Bernard & Buss, Adrian, 2015. "Trading Fees and Slow-Moving Capital," CEPR Discussion Papers 10737, C.E.P.R. Discussion Papers.
    10. Christoph Czichowsky & Rémi Peyre & Walter Schachermayer & Junjian Yang, 2018. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," Post-Print hal-02373296, HAL.
    11. Czichowsky, Christoph Johannes & Peyre, Rémi & Schachermayer, Walter & Yang, Junjian, 2018. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," LSE Research Online Documents on Economics 85230, London School of Economics and Political Science, LSE Library.
    12. M. Mania & R. Tevzadze, 2008. "Backward Stochastic PDEs related to the utility maximization problem," Papers 0806.0240, arXiv.org.
    13. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the existence of shadow prices," Working Papers hal-00645980, HAL.
    14. 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.
    15. Christoph Czichowsky & Rémi Peyre & Walter Schachermayer & Junjian Yang, 2018. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," Finance and Stochastics, Springer, vol. 22(1), pages 161-180, January.
    16. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the Existence of Shadow Prices," Papers 1111.6633, arXiv.org, revised Jan 2013.
    17. Luciano Campi & Elyès Jouini & Vincent Porte, 2013. "Efficient portfolios in financial markets with proportional transaction costs," Post-Print halshs-00664074, HAL.
    18. 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.
    19. Erhan Bayraktar & Leonid Dolinskyi & Yan Dolinsky, 2020. "Extended weak convergence and utility maximisation with proportional transaction costs," Finance and Stochastics, Springer, vol. 24(4), pages 1013-1034, October.
    20. Christoph Czichowsky & R'emi Peyre & Walter Schachermayer & Junjian Yang, 2016. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," Papers 1608.01415, arXiv.org.

    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:eee:spapps:v:119:y:2009:i:5:p:1561-1579. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.