On behalf of the Scientific Committee of the "B. de Finetti Risk Seminars, Milano Lectures on the Mathematical Theory of Economics and Finance”, we are glad to invite you to participate at the following Lecture which will take place on Thursday, May 5, 2022 at 17.30 (see all details below).  

Walter Schachermayer
Universität Wien

Title: Martingale Transport, De March-Touzi paving, and stretched Brownian motion in ℝd

Abstract: In classical optimal transport, the contributions of Benamou–Brenier and Mc-Cann regarding the time-dependent version of the problem are cornerstones of the field and form the basis for a variety of applications in other mathematical areas. For µ,ν probability measures on ℝd, increasing in convex order, stretched Brownian motion [1] provides an analogue for the martingale version of this problem.

In dimension d=1 it was shown in [2] that any martingale transport decomposes into at most countably many invariant intervals and that this decomposition is universal. Extensions of this result to d≥2 were studied in [4], [5], [3].
We show that the dual optimization problem attached to a stretched Brownian motion induces the universal De March–Touzi paving [3] of ℝd.

Joint work with M. Beiglböck, J. Backhoff, and B. Tschiderer.
REFERENCES
[1] J. Backhoff-Veraguas, M. Beiglböck, M. Huesmann, and S. Källblad. Martingale Benamou-Brenier: a probabilistic perspective. Ann. Probab., 48(5):2258–2289, 2020.
[2] M. Beiglböck and N. Juillet. On a problem of optimal transport under marginal martingale constraints. Ann. Probab., 44(1):42–106, 2016.
[3] H. De March and N. Touzi. Irreducible convex paving for decomposition of multidimensional martingale transport plans. Ann. Probab., 47(3):1726–1774, 2019.
[4] N. Ghoussoub, Y.-H. Kim, and T. Lim. Structure of optimal martingale transport plans in general dimensions. Ann. Probab., 47(1):109–164, 2019.
[5] J. Obłój and P. Siorpaes. Structure of martingale transports in finite dimensions. arXiv:1702.08433, 2017.


Scientific Committee
Prof. Simone Cerreia-Vioglio (Univ. Bocconi)
Prof. Marco Frittelli (Univ. degli Studi di Milano)
Prof. Fabio Maccheroni (Univ. Bocconi)
Prof. Marco Maggis (Univ. degli Studi di Milano)
Prof. Massimo Marinacci (Univ. Bocconi)
Prof. Emanuela Rosazza Gianin (Univ. Milano-Bicocca)  
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