Optimal portfolios in the presence of stress scenarios A worst-case approach

  • Insurance companies and banks regularly have to face stress tests performed by regulatory instances. To model their investment decision problems that includes stress scenarios, we propose the worst-case portfolio approach. Thus, the resulting optimal portfolios are already stress test prone by construction. A central issue of the worst-case portfolio approach is that neither the time nor the order of occurrence of the stress scenarios are known. Even more, there are no probabilistic assumptions regarding the occurrence of the stresses. By defining the relative worst-case loss and introducing the concept of minimum constant portfolio processes, we generalize the traditional concepts of the indifference frontier and the indifference-optimality principle. We prove the existence of a minimum constant portfolio process that is optimal for the multi-stress worst-case problem. As a main result we derive a verification theorem that provides conditions on Lagrange multipliers and nonlinear ordinary differential equations that support the construction of optimal worst-case portfolio strategies. The practical applicability of the verification theorem is demonstrated via numerical solution of various worst-case problems with stresses. There, it is in particular shown that an investor who chooses the worst-case optimal portfolio process may have a preference regarding the order of stresses, but there may also be stress scenarios where he/she is indifferent regarding the order and time of occurrence.

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Author:Ralf KornORCiD, Lukas MüllerORCiD
Parent Title (English):Mathematics and Financial Economics
Publisher:Springer Nature - Springer
Document Type:Article
Language of publication:English
Date of Publication (online):2024/04/02
Year of first Publication:2021
Publishing Institution:Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
Date of the Publication (Server):2024/04/02
Page Number:33
First Page:153
Last Page:185
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Zweitveröffentlichung