IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v22y2019i04ns0219024919500195.html
   My bibliography  Save this article

Multi-Asset Worst-Case Optimal Portfolios

Author

Listed:
  • RALF KORN

    (Department of Mathematics, Technische Universität Kaiserslautern, Erwin-Schrödinger-Strasse, 67663 Kaiserslautern, Germany)

  • ELISABETH LEOFF

    (Department of Financial Mathematics, Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany)

Abstract

We generalize the worst-case portfolio approach of Korn & Wilmott (2002) to a multi-asset setting. The nonuniqueness of indifference strategies results in a much more complicated portfolio optimization problem as in the single risky asset framework. To determine the worst-case optimal portfolio processes we develop two new approaches, a Lagrangian multiplier approach in the log-utility case and a combined constrained HJB equation and indifference strategy approach for dealing with power-utility functions. Various examples illustrate remarkable effects and differences compared to the single risky asset setting, in particular the possibility for using some stocks for crash hedging and thereby allowing stock investment possibilities that are not present in the single-stock case.

Suggested Citation

  • Ralf Korn & Elisabeth Leoff, 2019. "Multi-Asset Worst-Case Optimal Portfolios," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-24, June.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:04:n:s0219024919500195
    DOI: 10.1142/S0219024919500195
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024919500195
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024919500195?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Sascha Desmettre & Ralf Korn & Frank Thomas Seifried, 2015. "Lifetime Consumption And Investment For Worst-Case Crash Scenarios," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-30.
    2. Ralf Korn & Olaf Menkens, 2005. "Worst-Case Scenario Portfolio Optimization: a New Stochastic Control Approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(1), pages 123-140, September.
    3. 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.
    4. Korn, Ralf, 2005. "Worst-case scenario investment for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 1-11, February.
    5. Ralf Korn & Paul Wilmott, 2002. "Optimal Portfolios Under The Threat Of A Crash," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 171-187.
    Full references (including those not matched with items on IDEAS)

    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. Lihua Chen & Ralf Korn, 2019. "Worst-case portfolio optimization in discrete time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(2), pages 197-227, October.
    2. Christoph Belak & Sören Christensen & Olaf Menkens, 2016. "Worst-Case Portfolio Optimization In A Market With Bubbles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-36, March.
    3. Engler, Tina & Korn, Ralf, 2014. "Worst-case portfolio optimization under stochastic interest rate risk," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 2(4), pages 469-488.
    4. Belak, Christoph & Christensen, Sören & Menkens, Olaf, 2014. "Worst-case optimal investment with a random number of crashes," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 140-148.
    5. Sascha Desmettre & Sebastian Merkel & Annalena Mickel & Alexander Steinicke, 2023. "Worst-Case Optimal Investment in Incomplete Markets," Papers 2311.10021, arXiv.org.
    6. Xiang Lin & Chunhong Zhang & Tak Siu, 2012. "Stochastic differential portfolio games for an insurer in a jump-diffusion risk process," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(1), pages 83-100, February.
    7. A Chunxiang & Shao Yi, 2018. "Worst-Case Investment Strategy with Delay," Journal of Systems Science and Information, De Gruyter, vol. 6(1), pages 35-57, February.
    8. Ralf Korn, 2008. "Optimal portfolios: new variations of an old theme," Computational Management Science, Springer, vol. 5(4), pages 289-304, October.
    9. Tina Engler & Ralf Korn, 2014. "Worst-Case Portfolio Optimization under Stochastic Interest Rate Risk," Risks, MDPI, vol. 2(4), pages 1-20, December.
    10. Kerstin Dächert & Ria Grindel & Elisabeth Leoff & Jonas Mahnkopp & Florian Schirra & Jörg Wenzel, 2022. "Multicriteria asset allocation in practice," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 349-373, June.
    11. 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.
    12. Baltas, I. & Dopierala, L. & Kolodziejczyk, K. & Szczepański, M. & Weber, G.-W. & Yannacopoulos, A.N., 2022. "Optimal management of defined contribution pension funds under the effect of inflation, mortality and uncertainty," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1162-1174.
    13. 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.
    14. Martin Herdegen & Sebastian Herrmann, 2017. "Strict Local Martingales and Optimal Investment in a Black-Scholes Model with a Bubble," Papers 1711.06679, arXiv.org.
    15. 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.
    16. Hong‐Chih Huang, 2010. "Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 451-472, June.
    17. Bilel Jarraya & Abdelfettah Bouri, 2013. "A Theoretical Assessment on Optimal Asset Allocations in Insurance Industry," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 2(4), pages 30-44, October.
    18. Korn, Ralf, 2005. "Worst-case scenario investment for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 1-11, February.
    19. Soren Christensen, 2011. "Optimal decision under ambiguity for diffusion processes," Papers 1110.3897, arXiv.org, revised Oct 2012.
    20. Bihary, Zsolt & Víg, Attila András, 2018. "Portfólióallokáció csődveszély esetén, korlátolt felelősség mellett [Portfolio allocation in case of failure risk in the presence of limited liability]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 711-725.

    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:wsi:ijtafx:v:22:y:2019:i:04:n:s0219024919500195. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.