Pathwise analysis of log-optimal portfolios
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915408071622656 |
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| author | Allan, Andrew L. Kwossek, Anna P. Liu, Chong Prömel, David J. |
| author_facet | Allan, Andrew L. Kwossek, Anna P. Liu, Chong Prömel, David J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18232 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pathwise analysis of log-optimal portfolios Allan, Andrew L. Kwossek, Anna P. Liu, Chong Prömel, David J. Mathematical Finance Probability Portfolio Management 91G10, 60L20 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. |
| title | Pathwise analysis of log-optimal portfolios |
| topic | Mathematical Finance Probability Portfolio Management 91G10, 60L20 |
| url | https://arxiv.org/abs/2507.18232 |