Wellposedness of second order reflected BSDEs: A new formulation

Abstract

The aim of this article is to provide a complete theory of second order reflected backward stochastic differential equation (2RBSDE). We reformulate the notion of 2RBSDE by introducing a new type of minimality condition. Unlike the previous works, our minimality condition is more reasonable in the sense that it is suitable for dynamics with any kind of generators and it allows us to consider the 2RBSDE as a natural extension of 2BSDE. We prove the existence and uniqueness of solution to the 2RBSDE under Lipschitz-type assumptions on the generator. Moreover, we apply the 2RBSDE to obtain the super-hedging price of American options in the uncertain, incomplete, nonlinear financial market.