Reflected Backward Stochastic Differential Equation with Locally Monotone Coefficient

Abstract

We study the existence and uniqueness of Reflected Backward Stochastic Differential Equation (RBSDE for short) with both monotone and locally monotone coefficient and squared integrable terminal data. This is done with a polynomial growth condition on the coefficient. An application to the homogenization of multivalued Partial Differential Equations (PDEs for short) is given.

Key Words:

• BSDE
• Yosida approximation
• Meyer–Zheng topology
• Viscosity solution of multivalued PDEs
• Perturbations of reflected BSDEs and multivalued PDEs

Mathematics Subject Classification:

• Primary 60H20
• Secondary 60H30

Acknowledgments

The first author was supported by DEF/CNRS, PICS 444. The second author was supported by CMIFM, A.I. MA/01/02. The third author was supported by CNRST Maroc/CNRS France, 8310–2000 and TWAS grant 98–199 RG/MATHS/AF/AC.

Notes

^aThis assumption is not a restriction since we can replace φ(y) by where ⟨y, y ₀*⟩ ∈ Gr(∂φ).