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Worst-Case Portfolio Optimization In A Market With Bubbles

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  • CHRISTOPH BELAK

    (Department IV – Mathematics, University of Trier, Universitätsring 19, 54296 Trier, Germany)

  • SÖREN CHRISTENSEN

    (Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University, SE-412 96 Göteborg, Sweden)

  • OLAF MENKENS

    (School of Mathematical Sciences, Dublin City University, Collins Avenue, Dublin 9, Ireland)

Abstract

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.

Suggested Citation

  • Christoph Belak & Sören Christensen & Olaf Menkens, 2016. "Worst-Case Portfolio Optimization In A Market With Bubbles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-36, March.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:02:n:s0219024916500096
    DOI: 10.1142/S0219024916500096
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    References listed on IDEAS

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