Uniqueness and Existence of Linear Equilibrium with a Constrained Trader

TL;DR

This paper establishes the uniqueness and existence of linear equilibria in a discrete-time financial market with a constrained trader, connecting discrete and continuous-time models and supporting empirical observations.

Contribution

It proves the uniqueness of linear equilibrium structures based on demand expectations and confirms the existence of such equilibria in discrete-time markets.

Findings

Equilibrium structure is uniquely determined by two state variables.

Discrete-time equilibrium aligns with continuous-time models.

Existence of linear equilibrium is formally proven.

Abstract

We study a discrete-time financial market with a single constrained trader, competitive market makers, and noise traders. Within the class of linear equilibria, the equilibrium structure is shown to be uniquely determined by two state variables: the market maker's expectation of the trader's remaining demand and the residual demand beyond this expectation. This discrete-time uniqueness result aligns with its continuous-time analogue, indicating that the latter may emerge as the unique limit within the same class. We also prove the existence of a linear equilibrium, providing formal support to numerical and empirical findings in related work.