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Change of numeraire for weak martingale transport

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  • Beiglböck, Mathias
  • Pammer, Gudmund
  • Riess, Lorenz

Abstract

Change of numeraire is a classical tool in mathematical finance. Campi–Laachir–Martini (Campi et al., 2017) established its applicability to martingale optimal transport. We note that the results of Campi et al. (2017) extend to the case of weak martingale transport. We apply this to shadow couplings (in the sense of Beiglböck and Juillet (2021)), continuous time martingale transport problems in the framework of Huesmann–Trevisan (Huesmann and Trevisan, 2019) and in particular to establish the correspondence of stretched Brownian motion with its geometric counterpart. From a mathematical finance perspective, the geometric (stretched) Brownian motion and the corresponding geometric Bass local volatility model are more natural, and via the change of numeraire transform the efficient and well-understood algorithm for the Bass local volatility model can be adapted to this geometric counterpart.

Suggested Citation

  • Beiglböck, Mathias & Pammer, Gudmund & Riess, Lorenz, 2026. "Change of numeraire for weak martingale transport," Stochastic Processes and their Applications, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:spapps:v:192:y:2026:i:c:s0304414925002236
    DOI: 10.1016/j.spa.2025.104779
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    References listed on IDEAS

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    1. Beiglböck, Mathias & Henry-Labordère, Pierre & Touzi, Nizar, 2017. "Monotone martingale transport plans and Skorokhod embedding," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 3005-3013.
    2. Luciano Campi & Ismail Laachir & Claude Martini, 2017. "Change of numeraire in the two-marginals martingale transport problem," Finance and Stochastics, Springer, vol. 21(2), pages 471-486, April.
    3. Beatrice Acciaio & Antonio Marini & Gudmund Pammer, 2023. "Calibration of the Bass Local Volatility model," Papers 2311.14567, arXiv.org, revised Jul 2025.
    4. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglböck & Manu Eder, 2020. "Adapted Wasserstein distances and stability in mathematical finance," Finance and Stochastics, Springer, vol. 24(3), pages 601-632, July.
    5. Mathias Beiglboeck & Pierre Henry-Labordere & Nizar Touzi, 2017. "Monotone Martingale Transport Plans and Skorohod Embedding," Papers 1701.06779, arXiv.org.
    6. Pierre Henry-Labordère & Nizar Touzi, 2016. "An explicit martingale version of the one-dimensional Brenier theorem," Finance and Stochastics, Springer, vol. 20(3), pages 635-668, July.
    7. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglbock & Manu Eder, 2019. "Adapted Wasserstein Distances and Stability in Mathematical Finance," Papers 1901.07450, arXiv.org, revised May 2020.
    8. Acciaio, B. & Backhoff-Veraguas, J. & Zalashko, A., 2020. "Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization," LSE Research Online Documents on Economics 101864, London School of Economics and Political Science, LSE Library.
    9. Acciaio, B. & Backhoff-Veraguas, J. & Zalashko, A., 2020. "Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2918-2953.
    10. Campi, Luciano & Laachir, Ismail & Martini, Claude, 2017. "Change of numeraire in the two-marginals martingale transport problem," LSE Research Online Documents on Economics 68783, London School of Economics and Political Science, LSE Library.
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