Some analytically solvable problems of the mean-field games theory
Analysis of PDEs
2019-11-22 v1 Pricing of Securities
Abstract
We study the mean field games equations, consisting of the coupled Kolmogorov-Fokker-Planck and Hamilton-Jacobi-Bellman equations. The equations are complemented by initial and terminal conditions. It is shown that with some specific choice of data, this problem can be reduced to solving a quadratically nonlinear system of ODEs. This situation occurs naturally in economic applications. As an example, the problem of forming an investor's opinion on an asset is considered.
Cite
@article{arxiv.1911.09441,
title = {Some analytically solvable problems of the mean-field games theory},
author = {Sergey I. Nikulin and Olga S. Rozanova},
journal= {arXiv preprint arXiv:1911.09441},
year = {2019}
}
Comments
13 pages, 1 figure