  This paper studies function approximation for finite horizon discrete time
Markov decision processes under certain convexity assumptions. Uniform
convergence of these approximations on compact sets is proved under several
sampling schemes for the driving random variables. Under some conditions, these
approximations form a monotone sequence of lower or upper bounding functions.
Numerical experiments involving piecewise linear functions demonstrate that
very tight bounding functions for the fair price of a Bermudan put option can
be obtained with excellent speed (fractions of a cpu second). Results in this
paper can be easily adapted to minimization problems involving concave Bellman
functions.
