S. Then, Y g S,? (?) a.s. When for each n, ? n = ? a.s. , the result still holds without any assumption on

, Moreover, the converse statement holds

, 7) is equivalent to K ? ? ? ? Z ? a.s. Note that this constraint corresponds to the second constraint from (5.2)

, By similar arguments as those used in the proof of Theorem 7.18, it can be shown that the value process (Y t ) is a supersolution of the constrained reflected BSDE from Definition 7.15 with f replaced by g and the constraints (5.2) replaced by the constraint

Z. , K. , A. , and C. )-?-h,

, Y t ) is a supersolution of the above constrained reflected BSDE. Moreover, it is the minimal one

, Note that when ? = 0 and the obstacle is right-continuous, our result gives the existence of a minimal supersolution of the reflected BSDE with driver g, obstacle ? and with non positive jumps

, Moreover, our result provides a dual representation (with non linear expectation) of this minimal supersolution

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