Pathwise Portfolio Theory and Market Viability

Battle Count: 74

The paper provides deep theoretical foundations for model-free portfolio theory and market viability, which are relevant to robust quantitative trading. However, it is highly abstract and mathematical, with no empirical validation or practical trading algorithms. The insights about when classical equivalences break down (growth vs. viability separation) are important for understanding limitations of standard portfolio theory. The Föllmer calculus framework could inform pathwise trading strategy design, but implementation requires significant additional work.

Extremely high complexity. The paper requires deep knowledge of Föllmer pathwise integration, Faber-Schauder wavelet expansions, non-anticipative trend extraction, pseudo-inverse matrix operations, and scenario-wise measurability. Implementing the wealth-generating Föllmer portfolio class, the non-anticipative density selection, and the scenario-wise viability checks would require substantial mathematical programming expertise. No code or computational framework is provided.

This is a pure mathematics paper with complete formal proofs of all theorems, lemmas, and propositions. All definitions are self-contained, and the logical structure is fully specified. No empirical data or computational experiments are involved. The mathematical arguments can be independently verified from the text alone.