论文标题
奇异的无限尺寸汉密尔顿 - 雅各比 - 贝尔曼方程是由存储问题引起的
A singular infinite dimensional Hamilton-Jacobi-Bellman equation arising from a storage problem
论文作者
论文摘要
在本文的第一部分中，我们得出了一个无限的尺寸偏微分方程，该方程描述了一个存储模型中的经济平衡，其中包括无限数量的非原子剂。该方程式具有平均现场游戏主方程的形式。本文的第二部分致力于对汉密尔顿 - 雅各比 - 贝尔曼方程的数学研究，从中衍生出来。这个最后一个方程式既是奇异的又设置在希尔伯特空间上，因此增加了新的数学困难。
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.
