Solvability of the Gaussian Kyle model with imperfect information and risk aversion

TL;DR

This paper analyzes a Gaussian Kyle model with a risk-averse informed trader who has imperfect information, using optimal transport and filtering techniques to establish equilibrium conditions.

Contribution

It introduces a novel approach combining optimal transport and filtering to solve for equilibrium in a Gaussian Kyle model with risk aversion and imperfect information.

Findings

Equilibrium exists under the proposed framework.

Optimal transport characterizes the informed trader's utility.

Filtering under the historical measure is key to the solution.

Abstract

We investigate a Kyle model under Gaussian assumptions where a risk-averse informed trader has imperfect information on the fundamental price of an asset. We show that an equilibrium can be constructed by considering an optimal transport problem that is solved under a measure that renders the utility of the informed trader martingale and a filtering problem under the historical measure.