A partial stochastic equilibrium model and its limiting behaviour

TL;DR

This paper proves the existence of a market equilibrium in a finite-agent setting with exponential utility and analyzes the limiting behavior as the number of agents approaches infinity, showing the decoupling of the system and the deterministic influence of the mean field.

Contribution

It introduces a partial stochastic equilibrium model in a continuous-time setting and characterizes its limiting behavior as the number of agents grows large.

Findings

Existence of a market equilibrium price in a finite-agent model.

Decoupling of the BSDE system as agents tend to infinity.

Mean field influence becomes deterministic under common noise.

Abstract

The existence of a (partial) market equilibrium price is proved in a complete, continuous time finite-agent market setting. The economic agents act as price takers in a fully competitive setting and maximize exponential utility from terminal wealth. As the number $N$ of economic agents goes to infinity, the BSDE system of $N$ equations characterizing the equilibrium asset price dynamics decouples. Due to the system's symmetry, the influence of the mean field of the agents, conditionally on the common noise, becomes deterministic.