Discussion Papers 2022

CIRJE-F-1201	"Equilibrium Pricing of Securities in the Co-presence of Cooperative and Non-cooperative Populations"
Author Name	Fujii, Masaaki
Date	September 2022
Full Paper	PDF file
Remarks	Revised in June 2023; forthcoming in ESAIM: Control, Optimisation and Calculus of Variations.

Abstract
In this work, we develop an equilibrium model for price formation of securities in a market composed of two populations of different types: the first one consists of cooperative agents, while the other one consists of non-cooperative agents. The trading of every cooperative member is assumed to be coordinated by a central planner. In the large population limit, the problem for the central planner is shown to be a conditional extended mean-field control. In addition to the convexity assumptions, if the relative size of the cooperative population is small enough, then we are able to show the existence of a unique equilibrium for both the finite-agent and the mean-field models. The strong convergence to the mean-field model is also proved under the same conditions.
Keywords: market clearing, mean-eld games, extended mean-eld control, controlled-FBSDEs

Abstract

In this work, we develop an equilibrium model for price formation of securities in a market composed of two populations of different types: the first one consists of cooperative agents, while the other one consists of non-cooperative agents. The trading of every cooperative member is
assumed to be coordinated by a central planner. In the large population limit, the problem for the central planner is shown to be a conditional extended mean-field control. In addition to the convexity assumptions, if the relative size of the cooperative population is small enough, then we
are able to show the existence of a unique equilibrium for both the finite-agent and the mean-field models. The strong convergence to the mean-field model is also proved under the same conditions.

Keywords: market clearing, mean-eld games, extended mean-eld control, controlled-FBSDEs