Log-Optimal Portfolio

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. ...

Sequential Portfolio Selection under Latent Side Information-Dependence Structure: Optimality and Universal Learning Algorithms ArXiv ID: 2501.06701 “View on arXiv” Authors: Unknown Abstract This paper investigates the investment problem of constructing an optimal no-short sequential portfolio strategy in a market with a latent dependence structure between asset prices and partly unobservable side information, which is often high-dimensional. The results demonstrate that a dynamic strategy, which forms a portfolio based on perfect knowledge of the dependence structure and full market information over time, may not grow at a higher rate infinitely often than a constant strategy, which remains invariant over time. Specifically, if the market is stationary, implying that the dependence structure is statistically stable, the growth rate of an optimal dynamic strategy, utilizing the maximum capacity of the entire market information, almost surely decays over time into an equilibrium state, asymptotically converging to the growth rate of a constant strategy. Technically, this work reassesses the common belief that a constant strategy only attains the optimal limiting growth rate of dynamic strategies when the market process is identically and independently distributed. By analyzing the dynamic log-optimal portfolio strategy as the optimal benchmark in a stationary market with side information, we show that a random optimal constant strategy almost surely exists, even when a limiting growth rate for the dynamic strategy does not. Consequently, two approaches to learning algorithms for portfolio construction are discussed, demonstrating the safety of removing side information from the learning process while still guaranteeing an asymptotic growth rate comparable to that of the optimal dynamic strategy. ...

On Cost-Sensitive Distributionally Robust Log-Optimal Portfolio ArXiv ID: 2410.23536 “View on arXiv” Authors: Unknown Abstract This paper addresses a novel \emph{“cost-sensitive”} distributionally robust log-optimal portfolio problem, where the investor faces \emph{“ambiguous”} return distributions, and a general convex transaction cost model is incorporated. The uncertainty in the return distribution is quantified using the \emph{“Wasserstein”} metric, which captures distributional ambiguity. We establish conditions that ensure robustly survivable trades for all distributions in the Wasserstein ball under convex transaction costs. By leveraging duality theory, we approximate the infinite-dimensional distributionally robust optimization problem with a finite convex program, enabling computational tractability for mid-sized portfolios. Empirical studies using S&P 500 data validate our theoretical framework: without transaction costs, the optimal portfolio converges to an equal-weighted allocation, while with transaction costs, the portfolio shifts slightly towards the risk-free asset, reflecting the trade-off between cost considerations and optimal allocation. ...