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Worst-case portfolio optimization in discrete time

Author

Listed:
  • Lihua Chen

    (University of Kaiserslautern)

  • Ralf Korn

    (University of Kaiserslautern
    Fraunhofer ITWM)

Abstract

We consider discrete-time portfolio problems of an investor when taking the possibility of market crashes into account. In the case of the logarithmic utility function, we construct the worst-case optimal portfolio strategy by an indifference principle. Then, we extend the setting to general utility functions and derive the worst-case optimal portfolio processes via the characterization by a dynamic programming equation. Furthermore, we numerically examine the convergence behavior of the discrete-time worst-case optimal portfolio processes for the choice of popular utility functions when the time between two possible price changes tends to zero.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:90:y:2019:i:2:d:10.1007_s00186-019-00668-8
    DOI: 10.1007/s00186-019-00668-8
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    References listed on IDEAS

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    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    2. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. 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.
    5. Korn, Ralf, 2005. "Worst-case scenario investment for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 1-11, February.
    6. 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.
    7. Ralf Korn, 1997. "Optimal Portfolios:Stochastic Models for Optimal Investment and Risk Management in Continuous Time," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 3548, October.
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