Worst-case portfolio optimization in a market with bubbles

Christoph Belak, Sören Christensen, Olaf Menkens

Research output: Contribution to journalArticlepeer-review


We investigate a utility maximization problem in the presence of asset price bubbles. At random times, the investor receives warnings that a bubble has formed in the market which may lead to a crash in the risky asset. We propose a regime-switching model for the warnings and we make no assumptions about the distribution of the timing and the size of the crashes. Instead, we assume that the investor takes a worst-case perspective towards their impacts, i.e. the investor maximizes her expected utility under the worst-case crash scenario. We characterize the value function by a system of Hamilton-Jacobi-Bellman equations and derive a coupled system of ordinary differential equations for the optimal strategies. Numerical examples are provided.

Original languageEnglish
Article number1650009
JournalInternational Journal of Theoretical and Applied Finance
Issue number2
StatePublished - 1 Mar 2016
Externally publishedYes


  • Optimal investment
  • financial bubbles
  • market crashes
  • regime-switching
  • worst-case scenario


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