The robust Merton problem of an ambiguity averse investor
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We derive a closed form portfolio optimization rule for an investor who is diffident about mean return and volatility estimates, and has a CRRA utility. Confidence is here represented using ellipsoidal uncertainty sets for the drift, given a (compact valued) volatility realization. This specification affords a simple and concise analysis, as the agent becomes observationally equivalent to one with constant, worst case parameters. The result is based on a max–min Hamilton–Jacobi–Bellman–Isaacs PDE, which extends the classical Merton problem and reverts to it for an ambiguity-neutral investor.
KeywordsRobust optimization Merton problem Volatility uncertainty Ellipsoidal uncertainty on mean returns Hamilton–Jacobi–Bellman–Isaacs equation
Mathematics Subject Classification91G10 91B25 90C25 90C46 90C47
JEL ClassificationG11 C61
We sincerely thank Fausto Gozzi, Paolo Guasoni and Francesco Russo. Part of this research has been conducted while Sara Biagini was visiting the London School of Economics and Political Sciences, and special thanks go to Constantinos Kardaras for a number of precious conversations on the topic.
Conflict of interest
The authors declare that they have no conflict of interest
- 8.Fabozzi, F.J., Kolm, P.N., Pachamanova, D.A., Focardi, S.M.: Robust Portfolio Optimization and Management. Wiley, New York (2007)Google Scholar
- 12.Föllmer, H., Schied, A., Weber, S.: Robust preferences and robust portfolio choice. In Ciarlet, P, Bensoussan, A, Zhang, Q, (eds) Mathematical Modelling and Numerical Methods in Finance. Handbook of Numerical Analysis vol 15, pp. 29-88, (2009)Google Scholar
- 20.Neufeld, A., Nutz, M.: Robust utility maximization with Lévy Processes. Math. Financ. (accepted)Google Scholar
- 21.Nutz, M.: Utility maximization under model uncertainty in discrete time. Math. Financ. 26(2), 252–268 (2016)Google Scholar
- 25.Lin, Q., Riedel, F.: Optimal consumption and portfolio choice with ambiguity, Working paper, Center for Mathematical Economics, University of Bielefeld, (2014)Google Scholar