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Course Description
This course offers a whistle stop tour of several variants of the optimal transport problem that were introduced recently, often motivated by applications on stochastic analysis and mathematical finance. We plan to give an overview of the field with enough details for the participants to come out with a mental map of this fascinating research landscape and pointers for further individual studies. Accordingly, for each of our X-OT problems, we will provide an introduction, some fundamental theoretical results alongside with motivating applications and/or numerical methods allowing to implement and use these techniques.
In particular, we plan to consider
the classical Optimal Transport (OT) problem and the resulting distances on the space of probability measures, and their applications in distributionally robust optimization;
the Martingale Optimal Transport (MOT) and its relation to robust pricing and hedging problems;
the Adapted/Causal Optimal Transport (AOT) and its relation to continuity of stochastic control problems w.r.t. the law of the process;
the Entropic Optimal Transport (EOT) problem and its applications to numerical methods, including the Sinkhorn algorithm;
the Weak Optimal Transport (WOT) and its relation to stretched Brownian motions;
the Semimartingale Optimal Transport (SOT) and its applications to model calibration.
Program
Sunday January 26
16:00 - 17:00 Registration and opening remarks
17:00 - 19:00 Talks by participants
17:00 – 17:30 Johannes Wiesel “Sparsity of Quadratically Regularized Optimal Transport: Bounds on concentration and bias”
17:30 – 18:00 Annemarie Grass “Computable Root and Rost solutions to the multi-marginal Skorokhod embedding problem enabling an empirical study on robust prices of variance options”
18:00 – 18:30 Mattia Martini “Quantitative convergence for mean field control with degenerate idiosyncratic noise”
18:30 – 19:00 Alessandro Pinzi “Nested superposition principle: from the continuity equation over random measures to interacting particle systems”
Monday January 27
14:30 - 15:45 Lecture: Beatrice Acciaio - Classical Optimal Transport
15:45 - 16:15 Coffee break
16:15 - 17:30 Lecture: Jan Obłój - Distributionally Robust Optimization (DRO)
17:45 - 19:25 Talks by participants
17:45 – 18:10 Lukasz Szpruch “Linear convergence of proximal descent schemes on the Wasserstein space”
18:10 – 18:35 Anna De Crescenzo “Mean-field control of non exchangeable systems”
18:35 – 19:00 Antonello Pesce “Nash equilibrium in a singular stochastic game between two renewable power producers with price impact”
Tuesday January 28
10:00 - 12:00 Talks by participants
10:00 - 10:30 Robert Boyce “Unwinding Toxic Flow with Partial Information”
10:30 – 11:00 Marta Gentiloni Silveri “Theoretical guarantees in KL for Diffusion Flow Matching”
11:00 – 11:30 Giacomo Lucertini “Strong regularization by noise for a class of kinetic SDEs driven by symmetric α-stable processes”
11:30 – 12:00 Alessio Rondelli "Existence and uniqueness results for strongly degenerate McKean-Vlasov equations with rough coefficients"
14:30 - 15:45 Lecture: Jan Obłój - Martingale Optimal Transport (MOT)
15:45 - 16:15 Coffee break and Poster session
16:15 - 17:30 Lecture: Beatrice Acciaio - Weak Optimal Transport (WOT) and strecthed Brownian motion (SBM)
17:45 - 19:25 Talks by participants
17:45 – 18:10 Marius Chevallier “An Optimal Transport Approach to Arbitrage Correction: Application to Volatility Stress-Tests”
18:10 – 18:35 Stefan Schrott “Dual Attainment for Weak Optimal Transport”
18:35 – 19:00 Antonio Ocello “Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean Field Games”
19:00 – 19:25 Florin Suciu “A gradient flow on control space with rough initial condition”
Wednesday January 29
15:30 - 16:00 Coffee break
16:00 - 17:15 Lecture: Jan Obłój - PDE side, SgBM, Semimartingale Optimal Transport (SOT)
17:45 - 19:00 Lecture: Jan Obłój - Calibration/Numerics
Thursday January 30
15:00 - 16:15 Lecture: Beatrice Acciaio - Causal Optimal Transport and applications in finance
16:15 - 16:45 Coffee break
16:45 - 18:00 Lecture: Beatrice Acciaio - Adapted Optimal Transport and applications in finance
18:15 - 19:30 Talks by participants
18:15 – 18:40 Vlad Tuchilus “Optimal Transport with Causal Structures”
18:40 – 19:05 Giacomo Sodini “A relaxation viewpoint to Unbalanced Optimal Transport: Duality, optimality and Monge formulation”
19:05 – 19:30 Sturmius Tuschmann “Optimal Portfolio Choice with Cross-Impact”
Friday January 31
From 15:00 Closing remarks and round table
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