Convex Order and Arbitrage
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914071508418560 |
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| author | Zhang, Erica |
| author_facet | Zhang, Erica |
| contents | Wiesel and Zhang [2023] established that two probability measures $μ,ν$ on $\mathbb{R}^d$ with finite second moments are in convex order (i.e. $μ\preceq_c ν$) if and only if $W_2(ν,ρ)^2-W_2(μ,ρ)^2 \leq \int |y|^2ν(dy) - \int |x|^2μ(dx).$ Let us call a measure $ρ$ maximizing $W_2(ν,ρ)^2-W_2(μ,ρ)^2$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convex Order and Arbitrage Zhang, Erica Mathematical Finance Wiesel and Zhang [2023] established that two probability measures $μ,ν$ on $\mathbb{R}^d$ with finite second moments are in convex order (i.e. $μ\preceq_c ν$) if and only if $W_2(ν,ρ)^2-W_2(μ,ρ)^2 \leq \int |y|^2ν(dy) - \int |x|^2μ(dx).$ Let us call a measure $ρ$ maximizing $W_2(ν,ρ)^2-W_2(μ,ρ)^2$ 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. |
| title | Convex Order and Arbitrage |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2510.01599 |