Optimal Trading with Differing Trade Signals

TL;DR

This paper develops a mean-field game model for optimal trading where agents have subjective asset valuations, considering their impact on prices and the influence of shared or individual signals, providing insights into large-agent market dynamics.

Contribution

It introduces a mean-field game framework for multiple agents with subjective views, analyzing their trading strategies and market impact in a tractable way.

Findings

Derived mean-field equilibrium classifications.

Computed distribution of agents' inventories.

Analyzed how shared information affects price distribution.

Abstract

We consider the problem of maximizing portfolio value when an agent has a subjective view on asset value which differs from the traded market price. The agent's trades will have a price impact which affect the price at which the asset is traded. In addition to the agent's trades affecting the market price, the agent may change his view on the asset's value if its difference from the market price persists. We also consider a situation of several agents interacting and trading simultaneously when they have a subjective view on the asset value. Two cases of the subjective views of agents are considered, one in which they all share the same information, and one in which they all have an individual signal correlated with price innovations. To study the large agent problem we take a mean-field game approach which remains tractable. After classifying the mean-field equilibrium we compute the cross-sectional distribution of agents' inventories and the dependence of price distribution on the amount of shared information among the agents.