Maximum Principle for Control System driven by Mixed Fractional Brownian Motion

2023/12/19 by Yuhang Li, Li, Yuhang, Yuecai Han +1
Economics, Econometrics and Finance · #FOS: Mathematics #Financial Risk and Volatility Modeling #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2312.11893

openalex publication_date 2023/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the optimal control problem for systems driven by mixed fractional Brownian motion (including a fractional Brownian motion with Hurst parameter H>1/2 and the standard Brownian motion). By using Malliavin calculus and introducing a disturbance control region, we obtain a modified maximum principle. Through martingale representation theorem, we obtain the adjoint backward stochastic differential equation in a natural way. Furthermore, corresponding to [1], a significant result is that the necessary condition is simplified by only containing one equality. As an application, the linear quadratic case is investigated to illustrate the main results.

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