# Fully coupled mean-field FBSDEs with jumps and related optimal control problems

## TL;DR

This paper investigates fully coupled mean-field FBSDEs with jumps, establishing existence, uniqueness, and continuity of solutions, and applies these results to optimal control problems like mean-variance portfolio and linear-quadratic problems.

## Contribution

It introduces a comprehensive analysis of coupled mean-field FBSDEs with jumps, including solution properties and optimal control applications.

## Key findings

- Proved existence and uniqueness of solutions under monotonicity conditions
- Established the stochastic maximum principle for control problems
- Applied results to mean-variance and linear-quadratic portfolio problems

## Abstract

This paper study a type of fully coupled mean-field forward-backward stochastic differential equations with jumps under the monotonicity condition, including the existence and the uniqueness of the solution of our equation as well as the continuity property of the solutions with respect to the parameters. Then we establish the stochastic maximum principle for the corresponding optimal control problems and give the applications to mean-variance portfolio problems and linear-quadratic problems, respectively.