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KellyBoost: Growth-Optimal Portfolio Construction with Gradient-Boosted Trees

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  • Jiayu Li

Abstract

KellyBoost is a single multi-output XGBoost model whose softmax output is the portfolio: with y the vector of per-asset holding-period returns, the training loss is - log(1 + w y), the negative log growth rate, so the fitted model is the growth-optimal (Kelly) allocation conditioned on the features. The objective is exact rather than a surrogate: we derive the gradient, the analytic diagonal Hessian and the full Hessian in closed form, verify them by finite differences, and ship a dependency-free reference engine.

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  • Jiayu Li, 2026. "KellyBoost: Growth-Optimal Portfolio Construction with Gradient-Boosted Trees," Papers 2608.23393, arXiv.org.
    • Handle: RePEc:arx:papers:2608.23393
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    References listed on IDEAS

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    1. Shihao Gu & Bryan Kelly & Dacheng Xiu, 2020. "Empirical Asset Pricing via Machine Learning," Review of Finance, European Finance Association, vol. 33(5), pages 2223-2273.
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    3. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    4. L. C. MacLean & W. T. Ziemba & G. Blazenko, 1992. "Growth Versus Security in Dynamic Investment Analysis," Management Science, INFORMS, vol. 38(11), pages 1562-1585, November.
    5. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
    6. Hakansson, Nils H., 1971. "Capital Growth and the Mean-Variance Approach to Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(1), pages 517-557, January.
    7. Shihao Gu & Bryan Kelly & Dacheng Xiu, 2020. "Empirical Asset Pricing via Machine Learning," The Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2223-2273.
    8. A. Sinem Uysal & Xiaoyue Li & John M. Mulvey, 2024. "End-to-end risk budgeting portfolio optimization with neural networks," Annals of Operations Research, Springer, vol. 339(1), pages 397-426, August.
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