Backward stochastic differential equations with two barriers and generalized reflection

摘要

We prove the existence and uniqueness of solutions of backward stochastic differential equations (BSDEs) with generalized reflection at time dependent cadlag barriers. The reflection model we consider includes, as special cases, the standard reflection as well as the mirror reflection studied earlier in the theory of forward stochastic differential equations. We also show that the solution of BSDEs with generalized reflection corresponds to the value of an optimal stopping problem. (C) 2020 Elsevier B.V. All rights reserved.