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Optimal Portfolios Under The Threat Of A Crash

Author

Listed:
  • RALF KORN

    (Fachbereich Mathematik, Universität Kaiserslautern, 67653 Kaiserslautern, Germany)

  • PAUL WILMOTT

    (Wilmott Associates, London, UK)

Abstract

We consider the determination of optimal portfolios under the threat of a crash. Our main assumption is that upper bounds for both the crash size and the number of crashes occurring before the time horizon are given. We make no probabilistic assumption on the crash size or the crash time distribution. The optimal strategies in the presence of a crash possibility are characterized by a balance problem between insurance against the crash and good performance in the crash-free situation. Explicit solutions for the log-utility case are given. Our main finding is that constant portfolios are no longer optimal ones.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:05:y:2002:i:02:n:s0219024902001407
    DOI: 10.1142/S0219024902001407
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Ralf Korn, 2008. "Optimal portfolios: new variations of an old theme," Computational Management Science, Springer, vol. 5(4), pages 289-304, October.
    4. Soren Christensen, 2011. "Optimal decision under ambiguity for diffusion processes," Papers 1110.3897, arXiv.org, revised Oct 2012.
    5. Sascha Desmettre & Sebastian Merkel & Annalena Mickel & Alexander Steinicke, 2023. "Worst-Case Optimal Investment in Incomplete Markets," Papers 2311.10021, arXiv.org.
    6. 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.
    7. Esben Kryger & Maj-Britt Nordfang & Mogens Steffensen, 2020. "Optimal control of an objective functional with non-linearity between the conditional expectations: solutions to a class of time-inconsistent portfolio problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 405-438, June.
    8. Korn, Ralf, 2005. "Worst-case scenario investment for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 1-11, February.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Tina Engler & Ralf Korn, 2014. "Worst-Case Portfolio Optimization under Stochastic Interest Rate Risk," Risks, MDPI, vol. 2(4), pages 1-20, December.
    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. 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.
    17. Martin Herdegen & Sebastian Herrmann, 2017. "Strict Local Martingales and Optimal Investment in a Black-Scholes Model with a Bubble," Papers 1711.06679, arXiv.org.
    18. Sören Christensen, 2013. "Optimal decision under ambiguity for diffusion processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 207-226, April.
    19. 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.
    20. 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.

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