The Robust Merton Problem of an Ambiguity Averse Investor
Portfolio Management
2015-02-11 v1
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.
Keywords
Cite
@article{arxiv.1502.02847,
title = {The Robust Merton Problem of an Ambiguity Averse Investor},
author = {Sara Biagini and Mustafa Pinar},
journal= {arXiv preprint arXiv:1502.02847},
year = {2015}
}