Abstract: I will discuss resent results on error bounds for monotone approximation schemes for Hamilton-Jacobi-Bellman equations. These are second order degenerate elliptic and fully non-linear equations having non-smooth solutions. They appear in optimal stochastic control theory which has many applications e.g. in finance. For more than a decade, nobody was was able to obtain error bounds for numerical schemes for such equations. The breakthrough was made by Krylov in 1997 and 2000, and more recently these results have been improved and generalized by Barles and the speaker.
I will try to explain the ideas and some of the techniques involved and state the best result available. Then I will use this result to obtain the rate of convergence for a monotone finite difference method and give a brief discussion about the different existing results.