A Variational Approach For Price Formation Models In One Dimension

Abstract

In this paper, we study a class of first-order mean-field games (MFGs) that model price formation. Using Poincaré 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.

Equilibrium pricing of securities in the co-presence of cooperative and non-cooperative populations

“…Gomes & Saúde [34] present a deterministic model of electricity price formation. Different mathematical approaches and numerical calculation techniques on the same model are developed by Ashrafyan et al [6,7]. Its generalization with a random supply function is provided by Gomes et al [31].…”