Mean-field optimal control problem of SDDEs driven by fractional Brownian motion

2017/06/20 by Nacira Agram, Agram, Nacira, Soukaina Douissi +3
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR

paper · pdf · doi:10.48550/arxiv.1706.06233

20

openalex publication_date 2017/06/20 · arxiv created 2018/05/01 · arxiv updated 2018/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a mean-field optimal control problem for stochastic differential equations with delay driven by fractional Brownian motion with Hurst parameter greater than one half. Stochastic optimal control problems driven by fractional Brownian motion can not be studied using classical methods, because the fractional Brownian motion is neither a Markov process nor a semi-martingale. However, using the fractional White noise calculus combined with some special tools related to the differentiation for functions of measures, we establish and prove necessary and sufficient stochastic maximum principles. To illustrate our study, we consider two applications: we solve a problem of optimal consumption from a cash flow with delay and a linear-quadratique (LQ) problem with delay.

Related

• Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem
• Maximum Principle for Control System driven by Mixed Fractional Brownian Motion
• Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions
• The Global Maximum Principle for Optimal Control of Partially Observed Stochastic Systems Driven by Fractional Brownian Motion
• Optimal control of a stochastic network driven by a fractional Brownian motion input