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

Charles Bertucci (1) , Jean-Michel Lasry (2) , Pierre Louis Lions (2, 3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 Collège de France - Chaire Équations aux dérivées partielles et applications

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.

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Charles Bertucci, Jean-Michel Lasry, Pierre Louis Lions. A singular infinite dimensional Hamilton-Jacobi-Bellman equation arising from a storage problem. 2022. ⟨hal-03799871v1⟩