Kyle-Back Models with risk aversion and non-Gaussian Beliefs

TL;DR

This paper develops a new framework for Kyle's continuous-time insider trading model incorporating risk aversion and non-Gaussian beliefs, using a coupled forward-backward stochastic system and optimal transport methods.

Contribution

It introduces a novel approach to establish equilibrium existence in Kyle's model with non-Gaussian beliefs and risk aversion through a coupled stochastic PDE system.

Findings

Proves well-posedness of the coupled system for small risk aversion.

Shows equilibrium properties depend on the risk aversion parameter.

Models non-Gaussian beliefs of market makers at final time.

Abstract

We show that the problem of existence of equilibrium in Kyle's continuous time insider trading model can be tackled by considering a forward-backward system coupled via an optimal transport type constraint at maturity. The forward component is a stochastic differential equation representing an endogenously determined state variable and the backward component is a quasilinear parabolic equation representing the pricing function. By obtaining a stochastic representation for the solution of such a system, we show the well-posedness of solutions and study the properties of the equilibrium obtained for small enough risk aversion parameter. In our model, the insider has exponential type utility and the belief of the market maker on the distribution of the price at final time can be non-Gaussian.