Anticipated backward stochastic evolution equations and maximum principle for path-dependent systems in infinite dimensions

2025/04/26 by Liu, Guomin, Song, Jian, Wang, Meng
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2504.18798

Abstract

For a class of path-dependent stochastic evolution equations driven by cylindrical Q-Wiener process, we study the Pontryagin's maximum principle for the stochastic recursive optimal control problem. In this infinite-dimensional control system, the state process depends on its past trajectory, the control is delayed via an integral with respect to a general finite measure, and the final cost relies on the delayed state.To obtain the maximum principle, we introduce a functional adjoint operator for the non-anticipative path derivative and establish the well-posedness of an anticipated backward stochastic evolution equation in the path-dependent form, which serves as the adjoint equation.

Citations

• Stochastic maximum principle for equations with delay: going to infinite dimensions to solve the non-convex case
• A general maximum principle for optimal control of stochastic differential delay systems
• Maximum principle for optimal control of stochastic evolution equations with recursive utilities
• Path-dependent SDEs in Hilbert spaces
• A Maximum Principle for Optimal Control of Stochastic Evolution Equations
• Stochastic maximum principle for optimal control of SPDEs
• General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions
• Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations
• Functional Itô calculus and stochastic integral representation of martingales
• Stochastic equations with delay: optimal control via BSDEs and regular solutions of Hamilton-Jacobi-Bellman equations
• Anticipated backward stochastic differential equations

Related

• Maximum principle for recursive optimal control problem of stochastic delay evolution equations
• Stochastic maximum principle for infinite dimensional control systems
• General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions
• Maximum principle for optimal control of stochastic evolution equations with recursive utilities
• Relationship between maximum principle and dynamic programming principle for recursive optimal control problem of stochastic evolution equations