Multivalued backward stochastic differential equations with local Lipschitz drift

Abstract

We deal with a one dimensional multivalued backward stochastic differential equation associated to the subdifferential ∂hof a lower semi-continuous convex function h, with a local lipschitz coefficient (drift). When the terminal value is bounded, we prove the existence of a solution by using a suitable approximation of the drift by a double sequence of lipschitz functions. The uniqueness is obtained under the condition that the drift is local Lipschitz in y and globally Lipschitz in z. The existence result is an extension to the multivalued setting of the work of Hamadene