We consider high order numerical schemes for second order Hamilton-Jacobi-Bellman (HJB) equations. For high order approximation schemes (where "high" stands for greater than one), the inevitable loss of monotonicity prevents the use of the classical theoretical results for convergence to viscosity solutions. We present a class of "filtered" schemes: a suitable local modification of the high order scheme is introduced by "filtering" it with a monotone one. The resulting scheme can be proven to converge and it still shows an overall high order behavior for smooth enough solutions. We give theoretical proofs of these claims and validate the results with numerical tests.