Information-minimizing stationary financial market dynamics

2025-07-24

AI Summary

This paper addresses the lack of a unified theoretical framework for financial market dynamics grounded in fundamental mathematical principles. Method: It models financial markets as independent, stationary scalar diffusion processes—interpreted as communication systems—and jointly constrains the risk-neutral and physical probability measures via relative entropy minimization. Contribution/Results: The work introduces, for the first time, a unifying characterization of the growth-optimal portfolio, minimum-variance portfolio, and numéraire as a squared radial Ornstein–Uhlenbeck process—exhibiting strict additivity and self-similarity. This yields closed-form dynamic solutions for all three canonical portfolios, exposing their intrinsic mathematical structure. The framework establishes a rigorous information-theoretic foundation for risk-neutral pricing and portfolio allocation, while forging a fundamental link between measure selection and market equilibrium at the intersection of information theory and mathematical finance.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Other Foundations of Machine Learning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Model financial market dynamics using stationary scalar diffusions
• Minimize joint information of risk-neutral and real-world measures
• Characterize market securities as squared radial Ornstein-Uhlenbeck processes

Innovation

• Models market with independent stationary scalar diffusions
• Minimizes joint information of risk-neutral pricing measure
• Represents securities as squared radial Ornstein-Uhlenbeck processes