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.
*LOCATION: *The seminar will be held on Thursday, May 5, 2022 at 17.30,
Aula di Rappresentanza, Dept. of Mathematics, Milano University, Via C.
Saldini 50, Milano.
A light reception will take place at 17.00.
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)