Relationship between maximum principle and dynamic programming principle for stochastic recursive optimal control problem under volatility uncertainty

DOI10.1002/oca.2988arXiv2210.05213MaRDI QIDQ6081020

Xiaojuan Li

Publication date: 25 October 2023

Published in: Optimal Control Applications and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.05213

zbMATH Keywords

maximum principlebackward stochastic differential equation\(G\)-expectationdynamic programming principlestochastic recursive optimal control

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Optimal stochastic control (93E20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Nonlinear processes (e.g., (G)-Brownian motion, (G)-Lévy processes) (60G65)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quasi-continuous random variables and processes under the \(G\)-expectation framework
• Dynamic programming principle for stochastic recursive optimal control problem driven by a \(G\)-Brownian motion
• Wellposedness of second order backward SDEs
• Stochastic verification theorem of forward-backward controlled systems for viscosity solutions
• Some properties on \(G\)-evaluation and its applications to \(G\)-martingale decomposition
• Martingale representation theorem for the \(G\)-expectation
• Function spaces and capacity related to a sublinear expectation: application to \(G\)-Brownian motion paths
• On representation theorem of \(G\)-expectations and paths of \(G\)-Brownian motion
• Optimal control with delayed information flow of systems driven by \(G\)-Brownian motion
• Backward stochastic differential equations driven by \(G\)-Brownian motion
• Comparison theorem, Feynman-Kac formula and Girsanov transformation for BSDEs driven by \(G\)-Brownian motion
• Stochastic maximum principle for optimal control with multiple priors
• Ambiguous volatility, possibility and utility in continuous time
• Multi-dimensional \(G\)-Brownian motion and related stochastic calculus under \(G\)-expectation
• Stochastic Maximum Principle for Stochastic Recursive Optimal Control Problem Under Volatility Ambiguity
• The connection between the maximum principle and dynamic programming in stochastic control
• Existence of an optimal control for stochastic control systems with nonlinear cost functional
• User’s guide to viscosity solutions of second order partial differential equations
• Backward Stochastic Differential Equations in Finance
• Connection between MP and DPP for Stochastic Recursive Optimal Control Problems: Viscosity Solution Framework in the General Case
• On the relationship between the stochastic maximum principle and dynamic programming in singular stochastic control^†
• Nonlinear Expectations and Stochastic Calculus under Uncertainty
• Relationship between maximum principle and dynamic programming principle for stochastic recursive optimal control problems of jump diffusions
• Stochastic maximum principle, dynamic programming principle, and their relationship for fully coupled forward-backward stochastic controlled systems

This page was built for publication: Relationship between maximum principle and dynamic programming principle for stochastic recursive optimal control problem under volatility uncertainty