  We combine forward investment performance processes and ambiguity averse
portfolio selection. We introduce the notion of robust forward criteria which
addresses the issues of ambiguity in model specification and in preferences and
investment horizon specification. It describes the evolution of time-consistent
ambiguity averse preferences.
  We first focus on establishing dual characterizations of the robust forward
criteria. This offers various advantages as the dual problem amounts to a
search for an infimum whereas the primal problem features a saddle-point. Our
approach is based on ideas developed in Schied (2007) and Zitkovic (2009). We
then study in detail non-volatile criteria. In particular, we solve explicitly
the example of an investor who starts with a logarithmic utility and applies a
quadratic penalty function. The investor builds a dynamical estimate of the
market price of risk $\hat \lambda$ and updates her stochastic utility in
accordance with the so-perceived elapsed market opportunities. We show that
this leads to a time-consistent optimal investment policy given by a fractional
Kelly strategy associated with $\hat \lambda$. The leverage is proportional to
the investor's confidence in her estimate $\hat \lambda$.
