OPTIMAL PORTFOLIO CHOICE WITH CRASH AND DEFAULT RISK

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

International Journal of Theoretical and Applied Finance (IJTAF), 2022, vol. 25, issue 04n05, 1-31

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.

Keywords: Optimal portfolios; crash; default; worst-case scenario; minimum constant portfolio; constrained optimization (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0219024922500236

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