Two-barriers reflected backward doubly SDEs beyond right continuity

Abstract In this paper, we formulate a specific kind of reflected backward doubly stochastic differential equation with two barriers not necessarily right continuous. We prove the existence and uniqueness of the solution under Mokobodzki’s condition on the barriers and a Lipschitz driver through a Picard’s iteration method in an appropriate Banach space. Moreover, we show that the solution of such equations is characterized in terms of the value function of an extension of the corresponding stochastic Dynkin game.