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.
Keywords: Càdlàg Rough Paths, Itô Diffusion Process, Log-Optimal Portfolio, Pathwise Stability, Time-Discretization, Portfolio Management
Complexity vs Empirical Score
- Math Complexity: 9.5/10
- Empirical Rigor: 1.5/10
- Quadrant: Lab Rats
- Why: The paper is heavily mathematical, employing advanced concepts like càdlàg rough paths, Itô diffusions, and deterministic rough differential equations, with extensive theoretical derivations and proofs. There is no empirical data, backtesting, or implementation details; the analysis is purely theoretical and pathwise, focusing on stability and approximation properties rather than practical application.
flowchart TD
A["Research Goal<br>Pathwise Analysis of Log-Optimal Portfolios"] --> B["Methodology: Càdlàg Rough Paths"]
B --> C["Input: Itô Diffusion Market Model"]
C --> D["Computation: Pathwise Portfolio Construction"]
D --> E["Stability Analysis<br>Parameter Sensitivity"]
D --> F["Approximation Analysis<br>Time-Discretization Error"]
E --> G["Key Findings:<br>Deterministic Framework & Stability Estimates"]
F --> G