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Lifetime Consumption And Investment For Worst-Case Crash Scenarios

Author

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  • SASCHA DESMETTRE

    (Department of Mathematics, University of Kaiserslautern, Erwin-Schrödinger-Straße, 67663 Kaiserslautern, Germany)

  • RALF KORN

    (Department of Mathematics, University of Kaiserslautern, Erwin-Schrödinger-Straße, 67663 Kaiserslautern, Germany;
    Department of Financial Mathematics, Fraunhofer Institute for Industrial Mathematics, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany)

  • FRANK THOMAS SEIFRIED

    (Department of Mathematics, University of Kaiserslautern, Erwin-Schrödinger-Straße, 67663 Kaiserslautern, Germany)

Abstract

We investigate worst-case optimal consumption and portfolio decisions under the threat of a market crash on an infinite time horizon. We provide a closed-form solution for constant relative risk aversion and establish a rigorous verification result. More specifically, using martingale arguments we demonstrate that the optimal consumption-portfolio strategy can be characterized as the indifference strategy that achieves the best performance in the no-crash scenario. In addition, we find a dual characterization of the optimal strategy as the indifference strategy that minimizes the crash exposure. Finally, we quantify the impact of the crash on consumption and portfolio choice and analyze it in terms of the investor's risk and time preferences and prudence.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:01:n:s0219024915500041
    DOI: 10.1142/S0219024915500041
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    References listed on IDEAS

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    1. Robert J. Barro & Jose F. Ursua, 2008. "Macroeconomic Crises since 1870," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 39(1 (Spring), pages 255-350.
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    Cited by:

    1. 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.
    2. 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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