SoSe21

Stochastic Mass Transport SS2021

See here (under preprints) for the script of the course

ABOUT THE EXAM: Send me an email and we can coordinate an appointment. The exam will be oral, with a preference towards 'in person' rather than online. I will give you precise instructions concerning the precautions to be taken so that we're on the safe side (concerning Covid). The emphasis of the exam is on concepts and intuitions. The chapter on Skorokhod embedding in the lecture notes is NOT part of this exam.

CHAPTER I: Optimal Transport

Here a Link to a YouTube channel created by Alexander Posch, fellow student, illustrating Wasserstein geodesics between black-and-white images. Thanks Alexander!

You may find here and here lecture notes, slides, and codes, pertaining the computational side of optimal transport as well as some machine learning applications.

Here a link to a minicourse series on Optimal Transport and Machine Learning, to be held online by the IMSI from July 6 to July 7.

Videos of the lectures on OT:

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CHAPTER II: Martingale Optimal Transport

Here for the seminal paper on the subject and here for the connection with mathematical finance. Concerning stretched Brownian motion click on the following link: 'Martingale Benamou Brenier.pdf'

Videos of the lectures on Martingale OT:

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CHAPTER IV: Causal Optimal Transport and Adapted Weak Topologies

See here for the seminal article, here for connections to finance and a flavour for the continuous-time picture, and here for a deep study of topological aspects. Concerning numerics you can check here and here for brute force approaches, respectively for causal and bicausal transport, and here for a statistical perspective.

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