Mean-Field Doubly Reflected Backward Stochastic Differential Equations

TL;DR

This paper investigates mean-field doubly reflected backward stochastic differential equations, establishing existence and uniqueness of solutions under various integrability conditions using fixed point and penalization methods.

Contribution

It introduces two different approaches for proving existence and uniqueness of solutions, expanding the theoretical understanding of these complex equations.

Findings

Existence and uniqueness proven for p-integrable data with p=1 or p>1.

Fixed point and penalization methods are both effective under different assumptions.

The two methods cover different sets of assumptions, broadening applicability.

Abstract

We study mean-field doubly reflected BSDEs. First, using the fixed point method, we show existence and uniqueness of the solution when the data which define the BSDE are $p$-integrable with $p=1$ or $p>1$. The two cases are treated separately. Next by penalization we show also the existence of the solution. The two methods do not cover the same set of assumptions.