Viscosity solutions to second order path-dependent Hamilton-Jacobi-Bellman equations and applications

DOI10.1214/23-aap1954arXiv2005.05309OpenAlexW4389674451MaRDI QIDQ6139687

Jianjun Zhou

Publication date: 19 January 2024

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.05309

zbMATH Keywords

optimal controlviscosity solutionspath-dependent stochastic differential equationspath-dependent Hamilton-Jacobi-Bellman equationsbackward stochastic Hamilton-Jacobi-Bellman equations

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Optimal stochastic control (93E20) Applications of stochastic analysis (to PDEs, etc.) (60H30) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Hamilton-Jacobi equations in optimal control and differential games (49L12)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations
• Viscosity solutions of fully nonlinear parabolic path dependent PDEs. I.
• Viscosity solutions of fully nonlinear parabolic path dependent PDEs. II
• Viscosity solutions of fully nonlinear elliptic path dependent partial differential equations
• Adapted solution of a backward stochastic differential equation
• On viscosity solution of functional Hamilton-Jacobi type equations for hereditary systems
• Decoupled mild solutions of path-dependent PDEs and integro PDEs represented by BSDEs driven by cadlag martingales
• \(G\)-expectation weighted Sobolev spaces, backward SDE and path dependent PDE
• Change of variable formulas for non-anticipative functionals on path space
• Adapted solution of a degenerate backward SPDE, with applications
• A weak version of path-dependent functional Itô calculus
• Viscosity solutions of obstacle problems for fully nonlinear path-dependent PDEs
• Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. III: Uniqueness of viscosity solutions for general second-order equations
• Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. I: The case of bounded stochastic evolutions
• Functional Itō calculus and stochastic integral representation of martingales
• Strong-viscosity solutions: classical and path-dependent PDEs
• Crandall-Lions viscosity solutions for path-dependent PDEs: the case of heat equation
• Path dependent Feynman-Kac formula for forward backward stochastic Volterra integral equations
• Pseudo-Markovian viscosity solutions of fully nonlinear degenerate PPDEs
• A martingale approach for fractional Brownian motions and related path dependent PDEs
• Weak solution for a class of fully nonlinear stochastic Hamilton-Jacobi-Bellman equations
• On viscosity solutions of path dependent PDEs
• Techniques of variational analysis
• BSDE, path-dependent PDE and nonlinear Feynman-Kac formula
• Stochastic Optimal Control in Infinite Dimension
• Stochastic Differential Games and Viscosity Solutions of Hamilton–Jacobi–Bellman–Isaacs Equations
• Viscosity Solutions of Hamilton-Jacobi Equations
• Stochastic Hamilton–Jacobi–Bellman Equations
• User’s guide to viscosity solutions of second order partial differential equations
• Backward Stochastic Differential Equations in Finance
• Comparison of Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Path-Dependent PDEs
• Viscosity Solutions of Stochastic Hamilton--Jacobi--Bellman Equations
• Second Order Hamilton--Jacobi Equations in Hilbert Spaces and Stochastic Boundary Control
• Functional Itô calculus
• Backward Stochastic Differential Equations

This page was built for publication: Viscosity solutions to second order path-dependent Hamilton-Jacobi-Bellman equations and applications