Optimal Transport for Stochastic Processes with Applications to Mathematical Finance

What it is about

You deal with modern methods of optimal transport and their applications in financial mathematics, probability, statistics and machine learning. A focus is on Optimal Transport for stochastic processes (causal/adapted OT), martingale OT, weak OT as well as on numerical procedures such as entropic regularization and estimation procedures. In the end you can understand the theoretical foundations (duality, regularity, geometric properties) and apply optimal-transport methods to problems of model-independent pricing and robust hedging in financial mathematics.

What you will be able to do

• Understanding advanced optimal-transport theory
• Mastery of duality and regularity questions
• Classifying geometric properties of transport solutions
• Application to model-independent pricing and robust hedging
• Knowledge of numerical procedures (e.g. entropic OT, estimation of OT maps)

What the module consists of

• VorlesungTransmission of theoretical foundations and derivations
• Übungsaufgaben / Exercise sheetsDeepening through problems and independent work
• ProgrammierübungenPractical implementation and numerical experiments

Teaching method

• Tafelvortrag / blackboarddetailed derivations and proofs for deeper understanding
• PDF Lecture NotesSupport for self-study and review
• ExercisesConsolidation of theory through problems
• Programming exercisesApplication and implementation of numerical methods