Generalized mean-field backward stochastic differential equations and related partial differential equations

Abstract

In this paper, we derive the existence and uniqueness of the solution for a new class of mean-field backward stochastic differential equations, which involves the integral with respect to a continuous increasing process. In addition, we study the generalized mean-field backward stochastic differential equations in a Markovian framework, that is, it is associated with a reflected McKean-Vlasov stochastic differential equation. This allows us to give a probabilistic formula for viscosity solution of a nonlocal partial differential equation with a nonlinear Neumann boundary condition.

Keywords:

• Backward stochastic differential equations
• reflected McKean-Vlasov equation
• partial differential equations
• Neumann boundary condition
• viscosity solution
• mean-field models

2010 Mathematics Subject Classifications:

• Primary: 60H10
• 60H30
• Secondary:35K65

Disclosure statement

No potential conflict of interest was reported by the author.