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Mathematics and Financial Economics

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26-03-2016

The robust Merton problem of an ambiguity averse investor

Authors: Sara Biagini, Mustafa Ç. Pınar

Published in: Mathematics and Financial Economics | Issue 1/2017

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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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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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Title: The robust Merton problem of an ambiguity averse investor
Authors: Sara Biagini
Mustafa Ç. Pınar
Publication date: 26-03-2016
Publisher: Springer Berlin Heidelberg
Published in: Mathematics and Financial Economics / Issue 1/2017
Print ISSN: 1862-9679
Electronic ISSN: 1862-9660
DOI: https://doi.org/10.1007/s11579-016-0168-6

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