Pathwise analysis of log-optimal portfolios
Pathwise analysis of log-optimal portfolios ArXiv ID: 2507.18232 “View on arXiv” Authors: Andrew L. Allan, Anna P. Kwossek, Chong Liu, David J. Prömel Abstract Based on the theory of càdlàg 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 Itô 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. ...