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Mathematics and Financial Economics

, Volume 11, Issue 1, pp 1–24 | Cite as

The robust Merton problem of an ambiguity averse investor

  • Sara BiaginiEmail author
  • Mustafa Ç. Pınar
Article

Abstract

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.

Keywords

Robust optimization Merton problem Volatility uncertainty Ellipsoidal uncertainty on mean returns Hamilton–Jacobi–Bellman–Isaacs equation 

Mathematics Subject Classification

91G10 91B25 90C25 90C46 90C47 

JEL Classification

G11  C61 

Notes

Acknowledgments

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Economics and FinanceLUISS G. CarliRomeItaly
  2. 2.Department of Industrial EngineeringBilkent UniversityBilkentTurkey

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