OT + X

The Kantorovich Initiative plans to offer regular online courses on Optimal Transport + ‘X’, where, in different iterations, ‘X’ is chosen from the many disciplines in which optimal transport (OT) places an important role, including economics and finance, data science/statistics, computation, biology, etc. These courses will have two main objectives: first, to introduce a wide range of students to the exciting and broadly applicable research area of optimal transport, and second, to explore more closely its applications in a particular field, which will vary from year to year (represented by ‘X’ in the title).

In Fall 2020 OT+Economics will be taught by Brendan Pass from University of Alberta. There will be additional guest lectures by experts in applications of OT in economics and finance. For registration and more details check out the PIMS notice or e-mail Prof. Pass at pass@ualberta.ca.

The first part of the course surveys the basic theory of optimal transport. Topics to be covered include:

  • formulation of the problem
  • Kantorovich duality theory,
  • existence and uniqueness theory,
  • c-monotonicity and structure of solutions,
  • discrete optimal transport.

The second part of the course develops applications in economics. A surprisingly wide variety of problems in economic theory and econometrics are naturally formulated in terms of optimal transport. One illustrative example is matching problems, in which agents on two sides of a market are matched together into pairs (think, for instance, of employers and employees). Other examples include estimation of incomplete information, multi-variate generalizations of quantiles used to study dependence structures between distributions, industrial organization (screening problems), contract theory (hedonic or discrete choice models), and financial engineering (estimating model free bounds on derivative pricing and optimizing portfolios).

In both parts, we aim to keep the presentation accessible to non-experts, so that students with no prior background in either optimal transport or economics can follow the course. Intended audience: Senior undergraduates, master’s and PhD students in quantitative disciplines, such as pure and applied mathematics, statistics, computer science, economics and engineering. Researchers in industry with a strong background in one of these areas are welcome to join.