Change of numeraire for weak martingale transport
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910482330288128 |
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| author | Beiglböck, Mathias Pammer, Gudmund Riess, Lorenz |
| author_facet | Beiglböck, Mathias Pammer, Gudmund Riess, Lorenz |
| contents | Change of numeraire is a classical tool in mathematical finance. Campi-Laachir-Martini established its applicability to martingale optimal transport. We note that the results of Campi-Laachir-Martini extend to the case of weak martingale transport. We apply this to shadow couplings, continuous time martingale transport problems in the framework of Huesmann-Trevisan and in particular to establish the correspondence between stretched Brownian motion with its geometric counterpart.
Note: We emphasize that we learned about the geometric stretched Brownian motion gSBM (defined in PDE terms) in a presentation of Loeper \cite{Lo23} before our work on this topic started. We noticed that a change of numeraire transformation in the spirit of \cite{CaLaMa14} allows for an alternative viewpoint in the weak optimal transport framework. We make our work public following the publication of Backhoff-Loeper-Obloj's work \cite{BaLoOb24} on arxiv.org. The article \cite{BaLoOb24} derives gSBM using PDE techniques as well as through an independent probabilistic approach which is close to the one we give in the present article. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07523 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Change of numeraire for weak martingale transport Beiglböck, Mathias Pammer, Gudmund Riess, Lorenz Probability Mathematical Finance Change of numeraire is a classical tool in mathematical finance. Campi-Laachir-Martini established its applicability to martingale optimal transport. We note that the results of Campi-Laachir-Martini extend to the case of weak martingale transport. We apply this to shadow couplings, continuous time martingale transport problems in the framework of Huesmann-Trevisan and in particular to establish the correspondence between stretched Brownian motion with its geometric counterpart. Note: We emphasize that we learned about the geometric stretched Brownian motion gSBM (defined in PDE terms) in a presentation of Loeper \cite{Lo23} before our work on this topic started. We noticed that a change of numeraire transformation in the spirit of \cite{CaLaMa14} allows for an alternative viewpoint in the weak optimal transport framework. We make our work public following the publication of Backhoff-Loeper-Obloj's work \cite{BaLoOb24} on arxiv.org. The article \cite{BaLoOb24} derives gSBM using PDE techniques as well as through an independent probabilistic approach which is close to the one we give in the present article. |
| title | Change of numeraire for weak martingale transport |
| topic | Probability Mathematical Finance |
| url | https://arxiv.org/abs/2406.07523 |