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Optimal Portfolio Choice With Crash And Default Risk

Author

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  • LUKAS MÃœLLER

    (Department of Mathematics, University of Kaiserslautern, Erwin-Schroedinger-Strasse, 67663 Kaiserslautern, Germany)

Abstract

We consider the worst-case scenario portfolio approach, introduced by Korn & Wilmott (2002), in a multi-asset setting, where asset defaults can occur in addition to asset crashes. In our model, the strictly risk-averse investor does not know which asset is affected by the worst-case scenario. Based on a reformulation of the value function we define the set of minimum constant portfolio processes. We prove the existence of such a process that solves the worst-case crash/ default portfolio problem. In particular, we prove the existence of a portfolio process that is optimal for the investor and at the same time makes him/ her indifferent to the time of occurrence of the worst possible crash or default scenario. The optimal portfolios are derived from solutions of non-linear differential equations. Therefore, we construct an algorithmic framework to analyze selected examples. These examples show the importance of adapting the portfolio process when considering such worst-case scenarios in the investment problem.

Suggested Citation

  • Lukas Mãœller, 2022. "Optimal Portfolio Choice With Crash And Default Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 25(04n05), pages 1-31, June.
    • Handle: RePEc:wsi:ijtafx:v:25:y:2022:i:04n05:n:s0219024922500236
    DOI: 10.1142/S0219024922500236
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