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Worst Case Portfolio Optimization and HJB-Systems


  • Ralf Korn

    (Fachbereich Mathematik, Universit├Ąt Kaiserslautern)

  • Mogens Steffensen

    (Department of Applied Mathematics and Statistics, University of Copenhagen)


We formulate a portfolio optimization problem as a game where the investor chooses a portfolio and his opponent, the market, chooses some market crashes. The asymmetry of the opponents' decision processes leads to a new and delicate generalization of the classical Hamilton-Jacob-Bellman equation in stochastic control. We characterize the optimal controls in general and specify them further in the cases of HARA, logarithmic, and exponential utility of the investor.

Suggested Citation

  • Ralf Korn & Mogens Steffensen, "undated". "Worst Case Portfolio Optimization and HJB-Systems," FRU Working Papers 2006/02, University of Copenhagen. Department of Economics. Finance Research Unit.
  • Handle: RePEc:kud:kuiefr:200602

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    continuous-time game; asymmetric decisions; market crash; utility optimization;

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