2025/10/02 by Zhang, Erica
#FOS: Economics and business #Mathematical Finance (q-fin.MF)
paper · doi:10.48550/arxiv.2510.01599
Wiesel and Zhang [2023] established that two probability measures μ,ν on ℝd with finite second moments are in convex order (i.e. μ\preceqc ν) if and only if W2(ν,ρ)2-W2(μ,ρ)2 ≤ ∫ |y|2ν(dy) - ∫ |x|2μ(dx). Let us call a measure ρ maximizing W2(ν,ρ)2-W2(μ,ρ)2 the optimal ρ. This paper summarizes key findings by Wiesel and Zhang, develops new algorithms enhancing the search of optimal ρ, and builds on the paper through constructing a model-independent arbitrage strategy and developing associated numerical methods via the convex function recovered from the optimal ρ through Brenier's theorem. In addition to examining the link between convex order and arbitrage through the lens of optimal transport, the paper also gives a brief survey of functionally generated portfolio in stochastic portfolio theory and offers a conjecture of the link between convex order and arbitrage between two functionally generated portfolios.