Worst-Case Portfolio Optimization in a Market with Bubbles
International Journal of Theoretical and Applied Finance, Vol. 19, No. 2, 1650009 (36 pages), 2016.
Posted: 4 Sep 2013 Last revised: 3 May 2016
Date Written: December 17, 2014
We study a portfolio optimization problem in a financial market which is under the threat of crashes. 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. That is, for each admissible trading strategy, we determine the crash scenario (including the no-crash scenario) which minimizes the investor’s expected utility from terminal wealth and then find the trading strategy which maximizes her utility in the worst-case scenario. We characterize the optimal value functions by a system of HJB equations and derive a coupled system of ordinary differential equations for the optimal strategies. We conclude with numerical examples.
Keywords: optimal investment, market crashes, worst-case scenario, regime switching, financial bubbles
JEL Classification: G11
Suggested Citation: Suggested Citation