Pathwise analysis of log-optimal portfolios

Andrew L. Allan, Anna P. Kwossek, Chong Liu and David J. Pr\"omel

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Abstract: Based on the theory of c\`adl\`ag rough paths, we develop a pathwise approach to analyze stability and approximation properties of portfolios along individual price trajectories generated by standard models of financial markets. As a prototypical example from portfolio theory, we study the log-optimal portfolio in a classical investment-consumption optimization problem on a frictionless financial market modelled by an It\^o diffusion process. We identify a fully deterministic framework that enables a pathwise construction of the log-optimal portfolio, for which we then establish pathwise stability estimates with respect to the underlying model parameters. We also derive pathwise error estimates arising from the time-discretization of the log-optimal portfolio and its associated capital process.

Date: 2025-07
New Economics Papers: this item is included in nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2507.18232

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