  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.
