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The robust Merton problem of an ambiguity averse investor

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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.

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Notes

  1. The inverses in fact will satisfy the opposite inequality for every x, in particular for \(x =\hat{mu}-r\mathbf {1}\)

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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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Authors and Affiliations

  1. Department of Economics and Finance, LUISS G. Carli, 00197, Rome, Italy

    Sara Biagini

  2. Department of Industrial Engineering, Bilkent University, 06800, Bilkent, Ankara, Turkey

    Mustafa Ç. Pınar

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  1. Sara Biagini
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  2. Mustafa Ç. Pınar
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Correspondence to Sara Biagini.

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Biagini, S., Pınar, M.Ç. The robust Merton problem of an ambiguity averse investor. Math Finan Econ 11, 1–24 (2017). https://doi.org/10.1007/s11579-016-0168-6

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  • DOI: https://doi.org/10.1007/s11579-016-0168-6

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