Schr\"odinger's problem 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.