# Mean-Field Backward-Forward SDE with Jumps and Storage problem in Smart Grids

## TL;DR

This paper establishes the existence and uniqueness of solutions for a coupled mean-field forward-backward stochastic differential equation system with jumps, and applies it to address storage problems in smart grids with unpredictable electricity production.

## Contribution

It introduces a novel mathematical framework for coupled mean-field FBSDEs with jumps and demonstrates its application to smart grid storage issues under uncertain production conditions.

## Key findings

- Proved existence and uniqueness of solutions for the coupled system.
- Applied the theoretical results to smart grid storage problems.
- Addressed the impact of meteorological unpredictability on electricity production.

## Abstract

In this paper, we prove the existence and uniqueness of the solution of a coupled Mean-Field Forward-Backward SDE system with Jumps. Then, we give an application in the field of storage problem in smart grids, studied in [4] in the case where the production of electricity is not predictable due, for example, to the changes in meteorological forecasts.