Information-minimizing stationary financial market dynamics

2025/07/24 by Eckhard Platen, Platen, Eckhard · 1 citation
Economics, Econometrics and Finance · #60G35 #62P05 #62P20 #Complex Systems and Time Series Analysis #FOS: Economics and business #Mathematical Finance (q-fin.MF)

paper · pdf · doi:10.48550/arxiv.2507.18395

openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

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.

Citations

• Benchmark-Neutral Risk-Minimization for insurance products and nonreplicable claims
• Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity
• The numeraire portfolio in semimartingale financial models
• A Theory for the Term Structure of Interest Rates

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