Schr\"odinger's problem with constraints

TL;DR

This paper explores a broad class of Schr"odinger-type bridges to model equilibrium scenarios with trading costs and default risk, connecting them to classical Kyle models.

Contribution

It introduces a generalized framework linking Schr"odinger bridges to equilibrium models with additional market frictions.

Findings

Bridges are solutions to Schr"odinger-type problems.

Equilibria with trading costs converge to classical Kyle model equilibria.

The approach broadens the modeling of market dynamics with constraints.

Abstract

Motivated by the connection between the Kyle equilibrium with static private signal and the Brownian bridge, we study a much broader class of bridges that allow one to consider more general equilibrium models, for example ones including trading costs and default risk. We show that such bridges are solutions to problems of the Schr\"odinger-type. Leveraging this connection, we obtain that the equilibria in models with trading costs converge to equilibria in the classical Kyle model.