2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210187In 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.ProbabilityComputational Finance60H10text