A mathematical study of the excess growth rate
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914122163027968 |
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| author | Campbell, Steven Wong, Ting-Kam Leonard |
| author_facet | Campbell, Steven Wong, Ting-Kam Leonard |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_25740 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A mathematical study of the excess growth rate Campbell, Steven Wong, Ting-Kam Leonard Information Theory Probability Mathematical Finance Portfolio Management 94A15, 94A17, 91G10, 91G80, 60F10, 62B10 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. |
| title | A mathematical study of the excess growth rate |
| topic | Information Theory Probability Mathematical Finance Portfolio Management 94A15, 94A17, 91G10, 91G80, 60F10, 62B10 |
| url | https://arxiv.org/abs/2510.25740 |