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Pathwise analysis of log-optimal portfolios

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  • Andrew L. Allan
  • Anna P. Kwossek
  • Chong Liu
  • David J. Promel

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.

Suggested Citation

  • Andrew L. Allan & Anna P. Kwossek & Chong Liu & David J. Promel, 2025. "Pathwise analysis of log-optimal portfolios," Papers 2507.18232, arXiv.org.
    • Handle: RePEc:arx:papers:2507.18232
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