WORST-CASE PORTFOLIO OPTIMIZATION IN A MARKET WITH BUBBLES

Christoph Belak (), Sören Christensen () and Olaf Menkens ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 02, 1-36

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.

Keywords: Optimal investment; market crashes; worst-case scenario; regime-switching; financial bubbles (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0219024916500096

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