English

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.

Keywords

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}
}
R2 v1 2026-06-28T02:55:01.306Z