A Variational Approach For Price Formation Models In One Dimension
Analysis of PDEs
2022-04-05 v1
Abstract
In this paper, we study a class of first-order mean-field games (MFGs) that model price formation. Using Poincar{\'e} Lemma, we eliminate one of the equations and obtain a variational problem for a single function. This variational problem offers an alternative approach for the numerical solution of the original MFGs system. We show a correspondence between solutions of the MFGs system and the variational problem. Moreover, we address the existence of solutions for the variational problem using the direct method in the calculus of variations. We end the paper with numerical results for a linear-quadratic model.
Keywords
Cite
@article{arxiv.2204.01398,
title = {A Variational Approach For Price Formation Models In One Dimension},
author = {Yuri Ashrafyan and Tigran Bakaryan and Diogo Gomes and Julian Gutierrez},
journal= {arXiv preprint arXiv:2204.01398},
year = {2022}
}
Comments
22 pages, 7 figures