On optimal control of forward backward stochastic differential equations

2017/01/29 by Fouzia Baghéry, Baghery, Fouzia, Nabil Khelfallah +5
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #60H10 #60H30 #93E20 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1701.08392

openalex publication_date 2017/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a control problem where the system is driven by a decoupled as well as a coupled forward-backward stochastic differential equation. We prove the existence of an optimal control in the class of relaxed controls, which are measure-valued processes, generalizing the usual strict controls. The proof is based on some tightness properties and weak convergence on the space D of càdlàg functions, endowed with the Jakubowsky S-topology. Moreover, under some convexity assumptions, we show that the relaxed optimal control is realized by a strict control.

Related

• Necessary and sufficient optimality conditions for relaxed and strict control problems of backward systems
• The strict and relaxed stochastic maximum principle for optimal control problem of backward systems
• A general stochastic maximum principle for optimal control problems of forward-backward systems
• Existence of an Optimal Control for a coupled FBSDE with a non degenerate diffusion coefficient
• On the relaxed mean-field stochastic control problem