Reflected BSDE with a constraint and its applications in an incomplete market

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. Then we an application on the pricing of American options in incomplete market.

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