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The Robust Merton Problem of an Ambiguity Averse Investor

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  • Sara Biagini
  • Mustafa Pinar

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. The novelty is that confidence is here represented using ellipsoidal uncertainty sets for the drift, given a volatility realization. This specification affords a simple and concise analysis, as the optimal portfolio allocation policy is shaped by a rescaled market Sharpe ratio, computed under the worst case volatility. 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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  • Sara Biagini & Mustafa Pinar, 2015. "The Robust Merton Problem of an Ambiguity Averse Investor," Papers 1502.02847, arXiv.org.
    • Handle: RePEc:arx:papers:1502.02847
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    References listed on IDEAS

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    Cited by:

    1. Ariel Neufeld & Marcel Nutz, 2015. "Robust Utility Maximization with L\'evy Processes," Papers 1502.05920, arXiv.org, revised Mar 2016.
    2. Ariel Neufeld & Mario Sikic, 2017. "Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty," Papers 1711.03875, arXiv.org, revised Apr 2019.
    3. Ariel Neufeld & Mario Sikic, 2016. "Robust Utility Maximization in Discrete-Time Markets with Friction," Papers 1610.09230, arXiv.org, revised May 2018.

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