We consider the problem of worst case performance estimation for a stochastic dynamic model in the presence of model uncertainty. This is cast as a nonclassical controlled diffusion problem. An infinite dimensional linear programming formulation is given and its dual is derived. The dual is successively approximated on a bounded domain by a semi-infinite and a finite linear program. This uses function approximation based on a reproducing kernel Hilbert space. Error analysis for the approximation is provided along with an estimate of the sample complexity.