  This paper addresses the question of how to invest in a robust growth-optimal
way in a market where the instantaneous expected return of the underlying
process is unknown. The optimal investment strategy is identified using a
generalized version of the principal eigenfunction for an elliptic second-order
differential operator, which depends on the covariance structure of the
underlying process used for investing. The robust growth-optimal strategy can
also be seen as a limit, as the terminal date goes to infinity, of optimal
arbitrages in the terminology of Fernholz and Karatzas [Ann. Appl. Probab. 20
(2010) 1179-1204].
