Optimal transportation and martingale optimal transportation in mathematical finance

Alessandro Doldi

Schedule and Venue

Alessandro Doldi
22–26 July 2024

More Information following soon

The aim of this crash course is to introduce optimal transportation problems and their applications in mathematical finance. We will see both the Monge's and Kantorovich's formulations of the optimal transportation problem, and delve into Kantorovich's celebrated duality. Subsequently, we will examine how the optimal transportation problem naturally emerges in financial contexts, particularly in the context of robust super-replication of options, leading us to the martingale optimal transportation problem. Finally, we will explore the effects of entropic-type penalizations in the former problems.

-C. Villani, Topics in optimal transportation. Grad. Stud. Math., 58 American Mathematical Society, Providence, RI, 2003.
-H. Föllmer; A. Schied. Stochastic finance. An introduction in discrete time. Fourth revised and extended edition. De Gruyter Grad. De Gruyter, Berlin, 2016.

Participants: The seminar is aimed at master students and can be credited for following modules:

  • WP16 Advanced Topics in Financial Mathematics C in PStO 2021
  • WP17 Advanced Topics in Financial Mathematics C in PStO 2019

Credits: 3 ECTS