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Published in:
An Introduction to Maximal Regularity for Parabolic Evolution Equations Read chapter Read first chapter

2021 | OriginalPaper | Chapter

HJB Equation, Dynamic Programming Principle, and Stochastic Optimal Control

Author : Andrzej Święch

Published in: Nonlinear Partial Differential Equations for Future Applications

Publisher: Springer Singapore

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Abstract

The paper is an extended version of lecture notes from a mini-course given by the author in the workshop Optimal Control and PDE in Tohoku University in 2017. The main objective of the lecture notes is to give a short but rigorous introduction to the dynamic programming approach to stochastic optimal control problems. The manuscript discusses, among other things, the classical necessary and sufficient conditions for optimality, properties of the value function, and it contains a proof of the dynamic programming principle, and a proof that the value function is a unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation.

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previous chapter Singular Limit Problem to the Keller-Segel System in Critical Spaces and Related Medical Problems—An Application of Maximal Regularity
next chapter Regularity of Solutions of Obstacle Problems –Old & New–
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Metadata
Title
HJB Equation, Dynamic Programming Principle, and Stochastic Optimal Control
Author
Andrzej Święch
Copyright Year
2021
Publisher
Springer Singapore
Book
Nonlinear Partial Differential Equations for Future Applications

Print ISBN: 978-981-334-821-9

Electronic ISBN: 978-981-334-822-6

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-981-33-4822-6_5

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