An Infinite-Dimensional Insider Trading Game

TL;DR

This paper extends Kyle's 1985 insider trading model to an infinite-dimensional setting with a continuum of assets, providing a comprehensive framework for understanding cross-asset information and trading strategies.

Contribution

It introduces an infinite-dimensional Bayesian trading game with a scalar fixed point equilibrium, bridging informed-trading theory and modern multi-asset markets.

Findings

Closed-form equilibrium trading strategies

Characterization of price impact across assets

Analysis of information efficiency in the model

Abstract

We generalize the seminal framework of Kyle (1985) to a many-asset setting, bridging the gap between informed-trading theory and modern trading practices. Specifically, we formulate an infinite-dimensional Bayesian trading game in which the informed trader's private information may concern arbitrary aspects of the cross-sectional payoff structure across a continuum of traded assets. In this general setting, we obtain a parsimonious equilibrium characterized by a single scalar fixed point, which yields closed-form characterizations of equilibrium trading strategy, price impact within and across markets, and the information efficiency of equilibrium prices.