  We consider the problem of robustly maximizing the growth rate of investor
wealth in the presence of model uncertainty. Possible models are all those
under which the assets' region $E$ and instantaneous covariation $c$ are known,
and where additionally the assets are stable in that their occupancy time
measures converge to a law with density $p$. This latter assumption is
motivated by the observed stability of ranked relative market capitalizations
for equity markets. We seek to identify the robust optimal growth rate, as well
as a trading strategy which achieves this rate in all models. Under minimal
assumptions upon $(E,c,p)$, we identify the robust growth rate with the
Donsker-Varadhan rate function from occupancy time Large Deviations theory. We
also prove existence of, and explicitly identify, the optimal trading strategy.
We then apply our results in the case of drift uncertainty for ranked relative
market capitalizations. Assuming regularity under symmetrization for the
covariance and limiting density of the ranked capitalizations, we explicitly
identify the robust optimal trading strategy in this setting.
