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401-4498-DRL 1 Credits DR D-MATH

Advances in Optimal Transport and Stochastics

Lecturers & Examiners: Prof. Dr. Beatrice Acciaio, Dr. Gudmund Pammer

Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger ( ) with the course number. The email should have the subject „Graduate course registration (ETH)“.

VVZ CR n/a

Last Updated: 2026-02-05 16:22:19

Abstract

We study recent developments of stochastic transport with applications to mathematical finance. In particular, we will cover weak transport, martingale transport, causal and adapted transport.

Objective

Understanding of the main results and tools from classical transport and from the different new kinds of transports; intuition behind the main concepts and understanding of the proofs of the main results; ability to apply tools from optimal transport for applications in mathematical finance.

Content

We start by recalling the main concepts and results from the classical optimal transport theory, providing intuition of the main ideas and understanding of the needed mathematical methods. We then focus on recent developments of stochastic transport with applications to mathematical finance. In particular, we will cover the following topics: weak transport (including the special cases of entropic transport and barycentric transport), martingale transport (especially in connection with model-independent finance and the Skorokhod Embedding problem), causal and adapted transport (also related to stability in mathematical finance, and with applications to filtration enlargement, equilibrium problems, quantification of arbitrage). We will motivate the introduction of these different kinds of optimal transport in order to deal with several problems especially in mathematical finance, as pricing and hedging in a model-independent framework, gauging the distance between financial models, accounting for model uncertainty.

Resources

Lecture Notes

lecture notes will be provided at the beginning of the semester

General Information

Language: English
Levels: DR

Examination

Type: ungraded semester performance

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type	Title	Time & Place	Hours
lecture	Advances in Optimal Transport and Stochastics	Mon 14:15-16:00 (HG D 1.1)	2 h weekly

Offered In

Doctorate Mathematics (More Information at: )
- Subject Specialisation (The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM.)
  - Graduate School (Official website of the Zurich Graduate School in Mathematics: )