Mean-field SDE driven by a fractional Brownian motion and related stochastic control problem

Abstract

We study a class of mean-field stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H\in (1/2,1)$ and a related stochastic control problem. We derive a Pontryagin type maximum principle and the associated adjoint mean-field backward stochastic differential equation driven by a classical Brownian motion, and we prove that under certain assumptions, which generalise the classical ones, the necessary condition for the optimality of an admissible control is also sufficient.

arXiv comment34 pages

References in corpus (2)

• Mean-field backward stochastic differential equations: A limit approach
• Peng's Maximum Principle for a Stochastic Control Problem Driven by a Fractional and a Standard Brownian Motion