Model‐free portfolio theory: A rough path approach

Based on a rough path foundation, we develop model-free approach to stochastic portfolio theory (SPT). Our allows handle significantly more general portfolios compared previous approaches based Föllmer integration. Without the assumption of any underlying probabilistic model, prove pathwise formula for relative wealth process, which reduces in special case functionally generated version so-called master classical SPT. We show that appropriately scaled asymptotic growth rate far reaching generalization Cover's universal controlled paths coincides with best retrospectively chosen within this class. provide several novel results concerning integration, and highlight advantages by showing (nonfunctionally generated) log-optimal an ergodic Itô diffusion setting have same as one.