Information-minimizing stationary financial market dynamics

TL;DR

This paper models financial market dynamics as an information-minimizing communication system using independent stationary diffusions, revealing new properties of securities and portfolios through Ornstein-Uhlenbeck processes.

Contribution

It introduces a novel framework for market dynamics based on information minimization and stationary diffusions, linking financial models with communication theory.

Findings

Market modeled as an information-minimizing communication system

Securities and portfolios follow squared radial Ornstein-Uhlenbeck processes

Identifies self-similarity and additivity in market dynamics

Abstract

The paper derives the dynamics of a financial market from basic mathematical principles. It models the market dynamics using independent stationary scalar diffusions, assumes the existence of its growth optimal portfolio (GOP), interprets the market as a communication system, and minimizes, in an information-theoretical sense, the joint information of the risk-neutral pricing measure with respect to the real-world probability measure. In this information-minimizing market, its basic independent securities, their sums, minimum variance portfolio, and GOP, as well as the GOP of the entire market, represent squared radial Ornstein-Uhlenbeck processes with additivity and self-similarity properties.