A singular infinite dimensional Hamilton-Jacobi-Bellman equation arising from a storage problem
Analysis of PDEs
2023-08-03 v2 Optimization and Control
Abstract
In the first part of this paper, we derive an infinite dimensional partial differential equation which describes an economic equilibrium in a model of storage which includes an infinite number of non-atomic agents. This equation has the form of a mean field game master equation. The second part of the paper is devoted to the mathematical study of the Hamilton-Jacobi-Bellman equation from which the previous equation derives. This last equation is both singular and set on a Hilbert space and thus raises new mathematical difficulties.
Cite
@article{arxiv.2210.02780,
title = {A singular infinite dimensional Hamilton-Jacobi-Bellman equation arising from a storage problem},
author = {Charles Bertucci and Jean-Michel Lasry and Pierre Louis Lions},
journal= {arXiv preprint arXiv:2210.02780},
year = {2023}
}