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Worst-Case Portfolio Optimization under Stochastic Interest Rate Risk

Author

Listed:
  • Tina Engler

    (Department of Mathematics, Martin Luther University Halle-Wittenberg, 06099 Halle(Saale), Germany)

  • Ralf Korn

    (Department of Mathematics, University of Kaiserslautern, Germany and Financial Mathematics, Fraunhofer ITWM, Fraunhofer Platz 1, 67663 Kaiserslautern, Germany)

Abstract

We investigate a portfolio optimization problem under the threat of a market crash, where the interest rate of the bond is modeled as a Vasicek process, which is correlated with the stock price process. We adopt a non-probabilistic worst-case approach for the height and time of the market crash. On a given time horizon [0; T], we then maximize the investor’s expected utility of terminal wealth in the worst-case crash scenario. Our main result is an explicit characterization of the worst-case optimal portfolio strategy for the class of HARA (hyperbolic absolute risk aversion) utility functions.

Suggested Citation

  • Tina Engler & Ralf Korn, 2014. "Worst-Case Portfolio Optimization under Stochastic Interest Rate Risk," Risks, MDPI, vol. 2(4), pages 1-20, December.
    • Handle: RePEc:gam:jrisks:v:2:y:2014:i:4:p:469-488:d:42983
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    References listed on IDEAS

    as
    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    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. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    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.
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    Cited by:

    1. Sascha Desmettre & Sebastian Merkel & Annalena Mickel & Alexander Steinicke, 2023. "Worst-Case Optimal Investment in Incomplete Markets," Papers 2311.10021, arXiv.org.

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