Reflected BSDE with a Constraint and a New Doob-Meyer Nonlinear   Decomposition
  In this paper, we study a type of reflected BSDE with a constraint and introduce a new kind of nonlinear expectation via BSDE with a constraint and prove the Doob-Meyer decomposition with respect to the super(sub)martingale introduced by this nonlinear expectation. We then apply the results to the pricing of American options in incomplete market. 
Shige Peng and Mingyu Xu