Paper: arXiv 2510.25740

Authors: Steven Campbell, Ting-Kam Leonard Wong

Abstract

We study the excess growth rate – a fundamental logarithmic functional arising in portfolio theory – from the perspective of information theory. We show that the excess growth rate can be connected to the Rényi and cross entropies, the Helmholtz free energy, L. Campbell’s measure of average code length and large deviations. Our main results consist of three axiomatic characterization theorems of the excess growth rate, in terms of (i) the relative entropy, (ii) the gap in Jensen’s inequality, and (iii) the logarithmic divergence that generalizes the Bregman divergence. Furthermore, we study maximization of the excess growth rate and compare it with the growth optimal portfolio. Our results not only provide theoretical justifications of the significance of the excess growth rate, but also establish new connections between information theory and quantitative finance.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is dense with advanced mathematical formalism, including axiomatic characterizations, connections to information theory, and large deviations, but contains no backtests, code, or empirical data—only a single theoretical figure.

Research Flowchart

  flowchart TD
  A["Research Goal: Axiomatic Characterization of Excess Growth Rate"] --> B["Methodology: Information Theory & Financial Math"]
  
  subgraph Inputs
      B --> C["Portfolio Theory Framework"]
      B --> D["Information Measures"]
  end

  subgraph Processes
      C --> E["Connect EGR to Relative Entropy & Jensen's Gap"]
      D --> E
      E --> F["Establish Bregman Divergence Generalization"]
      F --> G["Link EGR to Campbell's Code Length & Large Deviations"]
  end
  
  G --> H["Key Findings: Axiomatic Characterizations & EGR vs. GOP Comparison"]

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0 of 70 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.