In this talk we shall present numerical approximations of unbounded value functions associated to some stochastic control problems. We derive new error estimates for monotone schemes based on Markov chain approximations, with a special focus on the case of unbounded coefficients and unbounded, possibly discontinuous, terminal data. One motivation of this study consists in extending the level set approach to chance-constrained control problems. A precise analysis of the level-set approach is carried out and some numerical simulations are given to illustrate the approach.