Representation of solutions to 2BSDEs in an extended monotonicity setting

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.

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Representation of solutions to 2BSDEs in an extended monotonicity setting

Cited by 4 publications

References 34 publications

Doubly Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Coefficients

Doubly Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Coefficients

Representation of solutions to quadratic 2BSDEs with unbounded terminal values

Wellposedness of second order reflected BSDEs: A new formulation

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