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A singular infinite dimensional Hamilton-Jacobi-Bellman equation arising from a storage problem

Bertucci, Charles; Lasry, Jean-Michel; Lions, Pierre-Louis (2022), A singular infinite dimensional Hamilton-Jacobi-Bellman equation arising from a storage problem. https://basepub.dauphine.psl.eu/handle/123456789/24064

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Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
19
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Author(s)
Bertucci, Charles
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Lasry, Jean-Michel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lions, Pierre-Louis
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.