Pathwise analysis of log-optimal portfolios
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.
Keywords
Cite
@article{arxiv.2507.18232,
title = {Pathwise analysis of log-optimal portfolios},
author = {Andrew L. Allan and Anna P. Kwossek and Chong Liu and David J. Prömel},
journal= {arXiv preprint arXiv:2507.18232},
year = {2025}
}