## Optimal portfolios under the threat of a crash

• We consider the determination of optimal portfolios under the threat of a crash. Our main assumption is that upper bounds for both the crash size and the number of crashes occurring before the time horizon are given. We make no probabilistic assumption on the crash size or the crash time distribution. The optimal strategies in the presence of a crash possibility are characterized by a balance problem between insurance against the crash and good performance in the crash-free situation. Explicit solutions for the log-utility case are given. Our main finding is that constant portfolios are no longer optimal ones.

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Author: Ralf Korn, Paul Wilmott urn:nbn:de:hbz:386-kluedo-10612 Report in Wirtschaftsmathematik (WIMA Report) (64) Preprint English 2000 2000 Technische Universität Kaiserslautern 2000/08/28 Optimal portfolios ; crash modelling ; equilibrium strategies ; log-utility ; worst-case scenario Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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