Highlights:
- Researchers develop an axiomatic characterization of the excess growth rate from portfolio theory.
- The study reveals deep links between information theory concepts and financial mathematics.
- Introduces three theorems based on entropy, Jensen’s inequality, and logarithmic divergence.
- Offers insights for maximizing portfolio growth through information-theoretic measures.
TLDR:
A groundbreaking study by Steven Campbell and Ting-Kam Leonard Wong connects the concept of excess growth rate in portfolio theory with fundamental ideas in information theory, establishing new mathematical bridges between finance, entropy, and divergence measures.
In a pioneering contribution to quantitative finance and information theory, Steven Campbell and Ting-Kam Leonard Wong have presented a new mathematical framework that redefines how the excess growth rate—a key concept in portfolio theory—is understood. Their research, published on arXiv under the title *A Mathematical Study of the Excess Growth Rate*, provides an axiomatic and information-theoretic treatment of this logarithmic functional central to understanding portfolio performance.
The paper demonstrates how the excess growth rate is inherently tied to essential quantities in information theory such as Rényi entropy, cross entropy, and Helmholtz free energy. These relationships allow the authors to express growth rates in terms of measures that are typically used to analyze data transmission, uncertainty, and energy efficiency. Importantly, they provide three rigorous characterization theorems based on (i) relative entropy, (ii) the gap in Jensen’s inequality, and (iii) a generalized logarithmic divergence that extends the classical Bregman divergence, widely used in optimization and statistical inference.
Beyond theoretical insights, Campbell and Wong’s work explores how maximizing the excess growth rate compares to traditional approaches in constructing the growth-optimal portfolio. Their findings suggest that information-theoretic methods could enhance financial decision-making by providing a unified view of risk, return, and informational efficiency. This crossover between information theory and financial mathematics expands the foundation for future research in algorithmic trading, risk modelling, and automated portfolio management. The study not only bridges distinct mathematical domains but also offers practical implications for both economists and computer scientists striving to better understand and model uncertainty-driven systems.
Source:
Source:
Original research paper: Steven Campbell and Ting-Kam Leonard Wong, ‘A Mathematical Study of the Excess Growth Rate’, arXiv:2510.25740v1 [cs.IT], DOI: https://doi.org/10.48550/arXiv.2510.25740