Worst-case portfolio optimization in a market with bubbles
Artikel i vetenskaplig tidskrift, 2016

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.


Christoph Belak

Universitat Trier

Sören Christensen

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Olaf Menkens

Dublin City University

International Journal of Theoretical and Applied Finance

0219-0249 (ISSN)

Vol. 19 artikel nr 1650009-



Sannolikhetsteori och statistik