Connection between MP and DPP for Stochastic Recursive Optimal Control Problems: Viscosity Solution Framework in the General Case

DOI10.1137/16M1064957zbMath1373.93384arXiv1603.02595MaRDI QIDQ4588839

Tianyang Nie, Zhen Wu, Jing-Tao Shi

Publication date: 2 November 2017

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.02595

zbMATH Keywords

maximum principleviscosity solutionbackward stochastic differential equationdynamic programming principlestochastic recursive optimal controlsubjetssuperjets

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Dynamic programming (90C39) Optimal stochastic control (93E20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Optimality conditions for problems involving randomness (49K45)

Related Items (7)

Near-optimal control of stochastic recursive systems via viscosity solution ⋮ Linear-Quadratic-Gaussian Mixed Mean-Field Games with Heterogeneous Input Constraints ⋮ Relationship between maximum principle and dynamic programming principle for stochastic recursive optimal control problem under volatility uncertainty ⋮ Relationships between the maximum principle and dynamic programming for infinite dimensional stochastic control systems ⋮ Singular optimal controls for stochastic recursive systems under convex control constraint ⋮ A partially observed non-zero sum differential game of forward-backward stochastic differential equations and its application in finance ⋮ Stochastic maximum principle, dynamic programming principle, and their relationship for fully coupled forward-backward stochastic controlled systems

Cites Work

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• Stochastic verification theorem of forward-backward controlled systems for viscosity solutions
• Relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems and applications
• A general maximum principle for optimal control of forward-backward stochastic systems
• Relationship between MP and DPP for the stochastic optimal control problem of jump diffusions
• Adapted solution of a backward stochastic differential equation
• Quadratic BSDEs with convex generators and unbounded terminal conditions
• Maximum principle, dynamic programming and their connection in deterministic control
• Backward stochastic differential equations and partial differential equations with quadratic growth.
• Backward stochastic differential equations and applications to optimal control
• BSDE with quadratic growth and unbounded terminal value
• On the comparison theorem for multidimensional BSDEs
• Generalized Hamilton--Jacobi--Bellman Equations with Dirichlet Boundary Condition and Stochastic Exit Time Optimal Control Problem
• Optimality Variational Principle for Controlled Forward-Backward Stochastic Differential Equations with Mixed Initial-Terminal Conditions
• Erratum: "A Corrected Proof of the Stochastic Verification Theorem within the Framework of Viscosity Solutions"
• Stochastic Verification Theorems within the Framework of Viscosity Solutions
• A General Stochastic Maximum Principle for Optimal Control Problems
• Dynamic Programming Principle for One Kind of Stochastic Recursive Optimal Control Problem and Hamilton–Jacobi–Bellman Equation
• The connection between the maximum principle and dynamic programming in stochastic control
• A Generalized dynamic programming principle and hamilton-jacobi-bellman equation
• Stochastic Differential Utility
• User’s guide to viscosity solutions of second order partial differential equations
• An Introductory Approach to Duality in Optimal Stochastic Control
• Backward Stochastic Differential Equations in Finance
• The Pontryagin Maximum Principle From Dynamic Programming and Viscosity Solutions to First-Order Partial Differential Equations
• Stochastic maximum principle for optimal control problem of forward and backward system
• The Maximum Principles for Stochastic Recursive Optimal Control Problems Under Partial Information
• On a Class of Stochastic Optimal Control Problems Related to BSDEs with Quadratic Growth
• A Corrected Proof of the Stochastic Verification Theorem within the Framework of Viscosity Solutions

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