An optimal control problem for functional forward-backward stochastic systems and related Path-dependent HJB equations

2012/04/30 by Shaolin Ji, Ji, Shaolin, Shuzhen Yang +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #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.1204.6543

openalex publication_date 2012/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming principle and the related Path-dependent Hamilton-Jacobi-Bellman (HJB) equation in the framework of functional Itô calculus. The stochastic verification theorem for the smooth case is proved. Finally, we show that the value function is the viscosity solution of the Path-dependent HJB equation.

Related

• Path-dependent Hamilton-Jacobi-Bellman equations related to controlled stochastic functional differential systems
• Stochastic Recursive Optimal Control of McKean-Vlasov Type: A Viscosity Solution Approach
• Dynamic programming principle and Hamilton-Jacobi-Bellman equation under nonlinear expectation
• Path-Dependent Optimal Stochastic Control and Viscosity Solution of Associated Bellman Equations
• Stochastic differential game of functional forward-backward stochastic system and related path-dependent HJBI equation