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

2022/10/06 by Charles Bertucci, Bertucci, Charles, Jean‐Michel Lasry +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #Economic theories and models #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.2210.02780

openalex publication_date 2022/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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