Path-dependent Kyle equilibrium model

TL;DR

This paper extends the Kyle equilibrium model to include path-dependent price functions, using functional Itô calculus to establish conditions for equilibrium existence with both risk-neutral and risk-averse insiders.

Contribution

It introduces a path-dependent Kyle equilibrium model and applies functional Itô calculus to derive existence conditions, expanding the original Kyle framework.

Findings

Established necessary and sufficient conditions for equilibrium existence.

Extended Kyle model to path-dependent settings.

Analyzed both risk-neutral and risk-averse insider cases.

Abstract

We consider an auction type equilibrium model with an insider in line with the one originally introduced by Kyle in 1985 and then extended to the continuous time setting by Back in 1992. The novelty introduced with this paper is that we deal with a general price functional depending on the whole past of the aggregate demand, i.e. we work with path-dependency. By using the functional It\^o calculus, we provide necessary and sufficient conditions for the existence of an equilibrium. Furthermore, we consider both the cases of a risk-neutral and a risk-averse insider.