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Worst-case portfolio optimization in a market with bubbles
Belak, Christoph; Christensen, Sören; Menkens, Olaf
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.
Keyword(s): Finance; Probabilities; optimal investment; market crashes; worst-case scenario; regime switching; financial bubbles
Publication Date:
2016
Type: Other
Peer-Reviewed: Unknown
Language(s): English
Institution: Dublin City University
Citation(s): Belak, Christoph, Christensen, Sören and Menkens, Olaf (2016) Worst-case portfolio optimization in a market with bubbles. International Journal of Theoretical and Applied Finance, 19 (2). p. 1650009. ISSN 1793-6322
Publisher(s): World Scientific
File Format(s): application/pdf
Related Link(s): http://doras.dcu.ie/21135/1/BubblePaper_Final__OAV.pdf,
http://dx.doi.org/10.1142/S0219024916500096
First Indexed: 2017-03-18 05:58:39 Last Updated: 2019-02-09 06:18:44