Worst-case portfolio optimization in discrete time
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We consider discrete-time portfolio problems of an investor when taking the possibility of market crashes into account. In the case of the logarithmic utility function, we construct the worst-case optimal portfolio strategy by an indifference principle. Then, we extend the setting to general utility functions and derive the worst-case optimal portfolio processes via the characterization by a dynamic programming equation. Furthermore, we numerically examine the convergence behavior of the discrete-time worst-case optimal portfolio processes for the choice of popular utility functions when the time between two possible price changes tends to zero.
KeywordsWorst-case portfolio optimization Market crash Dynamic programming
Suggestions and constructive comments from the associate editor and an anonymous referee are gratefully acknowlegded.
- Hua P, Wilmott P (1997) Crash course. Risk Mag 10(6):64–67Google Scholar
- Kröner H (2014) Portfoliooptimierung im Binomialmodell. PhD thesis, University of KaiserslauternGoogle Scholar
- Menkens O (2004) Crash hedging strategies and optimal portfolios. PhD thesis, University of KaiserslauternGoogle Scholar
- Pliska SR (1997) Introduction to mathematical finance, discrete time models. Blackwell Publishers Inc, OxfordGoogle Scholar