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.
| Original language | English |
|---|---|
| Pages (from-to) | 703-731 |
| Number of pages | 29 |
| Journal | Mathematical Models and Methods in Applied Sciences |
| Volume | 35 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Mar 2025 |
Keywords
- Hamilton-Jacobi equations
- economic modeling
- infinite-dimensional partial differential equations
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