A Mathematical Study of the Excess Growth Rate

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Highly relevant to quantitative trading and portfolio management. The excess growth rate is a fundamental concept in stochastic portfolio theory, directly connected to rebalancing benefits, volatility harvesting, and the growth optimal (Kelly) portfolio. The optimization results (Theorems 4.2, 4.6) provide explicit solutions for maximizing excess growth rate and characterize the relationship with the classical growth optimal portfolio. The numeraire invariance property has direct implications for currency/asset denomination choices. However, the paper is primarily theoretical and does not present a complete trading system or empirical backtest.

The theoretical framework is mathematically sophisticated (axiomatic characterizations, functional equations, information geometry, large deviations). However, the key optimization results have explicit closed-form solutions: The deterministic maximizer (Theorem 4.2) is supported on exactly two assets (max and min log returns) with an explicit formula. The first-order condition for the stochastic case (Theorem 4.6) is a simple expectation inequality. The variational representation (Proposition 2.8) connects to standard convex optimization. Practical implementation of the portfolio optimization is straightforward; the complexity lies in understanding the theoretical underpinnings.

As a purely theoretical/mathematical paper with complete proofs, the results are fully reproducible by verification of the mathematical arguments. The paper provides explicit formulas for optimal solutions (Theorem 4.2), complete proofs of all theorems and lemmas, and a GitHub repository for the empirical illustration in Appendix A (Figure 2). However, there are no computational experiments or benchmarks to reproduce.