Solution to HJB equations with an elliptic integro-differential operator   and gradient constraint
  The main goal of this paper is to establish existence, regularity and uniqueness results for the solution of a Hamilton-Jacobi-Bellman (HJB) equation, whose operator is an elliptic integro-differential operator. The HJB equation studied in this work arises in singular stochastic control problems where the state process is a controlled $d$-dimensional L\'evy process. 
Harold A. Moreno-Franco
math.OC