This paper resolves a question proposed in Kardaras and Robertson (2011): how
to invest in a robust growth-optimal way in a market where precise knowledge of
the covariance structure of the underlying process is unavailable. Among an
appropriate class of admissible covariance structures, we characterize the
optimal trading strategy in terms of a generalized version of a principal
half-eigenvalue of a Pucci extremal operator and its associated eigenfunction.