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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
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    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)

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