Mathematical Methods of Operations Research

, Volume 90, Issue 2, pp 197–227 | Cite as

Worst-case portfolio optimization in discrete time

  • Lihua Chen
  • Ralf KornEmail author
Original Article


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.


Worst-case portfolio optimization Market crash Dynamic programming 



Suggestions and constructive comments from the associate editor and an anonymous referee are gratefully acknowlegded.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Department of Financial MathematicsFraunhofer ITWMKaiserslauternGermany

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