Two-barriers-reflected BSDE with Rank-based Data

We investigate two-barriers-reflected backward stochastic differential equations with data from rank-based stochastic differential equation. More specifically, we focus on the solution of backward stochastic differential equations restricted to two prescribed upper-boundary and lower-boundary processes. We rigorously show that this solution gives a probabilistic expression to the viscosity solution of some obstacle problems for the corresponding parabolic partial differential equations. As an application, the pricing problem of an American game option is studied.