  We study a maturity randomization technique for approximating optimal control
problems. The algorithm is based on a sequence of control problems with random
terminal horizon which converges to the original one. This is a generalization
of the so-called Canadization procedure suggested by Carr [Review of Financial
Studies II (1998) 597--626] for the fast computation of American put option
prices. In addition to the original application of this technique to optimal
stopping problems, we provide an application to another problem in finance,
namely the super-replication problem under stochastic volatility, and we show
that the approximating value functions can be computed explicitly.
