Mean-field reflected backward stochastic differential equations ☆
2012
In this paper, mean-field reflected backward stochastic differential equations (MF-RBSDEs, for short) are introduced and studied. We prove the existence and uniqueness of solutions for MF-RBSDEs under the Lipschitz condition by a fixed point argument. Under monotone assumptions for coefficients, we show a comparison theorem for MF-RBSDEs. We finally get an existence and a comparison theorem of the minimal solution when the coefficients are continuous, non-decreasing in y′ and have a linear growth.
Keywords:
- Peano existence theorem
- Comparison theorem
- Stochastic partial differential equation
- Initial value problem
- Picard–Lindelöf theorem
- Sturm separation theorem
- Arzelà–Ascoli theorem
- Mathematical optimization
- Sturm–Picone comparison theorem
- Mathematical analysis
- Mathematics
- Fixed-point theorem
- Brouwer fixed-point theorem
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