SEMI-LAGRANGIAN SCHEMES FOR LINEAR AND FULLY NON-LINEAR HAMILTON-JACOBI-BELLMAN EQUATIONS

(Communicated by the associate editor name) Abstract. We consider the numerical solution of Hamilton-Jacobi-Bellman equations arising in stochastic control theory. We introduce a class of mono-tone approximation schemes relying on monotone interpolation. These schemes converge under very weak assumptions, including the case of arbitrary degen-erate diffusions. Besides providing a unifying framework that includes several known first order accurate schemes, stability and convergence results are given, along with two different robust error estimates. Finally, the method is applied to a super-replication problem from finance. 1. Introduction. I