401-4498-23L  Advances in Optimal Transport and Stochastics

SemesterSpring Semester 2023
LecturersG. Pammer, B. Acciaio
Periodicitynon-recurring course
Language of instructionEnglish


AbstractWe study recent developments of stochastic transport with applications to mathematical finance. In particular, we will cover weak transport, martingale transport, causal and adapted transport.
ObjectiveUnderstanding 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.
ContentWe 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.
Lecture notesLecture notes will be provided at the beginning of the semester
Prerequisites / NoticeMeasure Theory, Probability and Stochastic Calculus (basic)