Search
Talk

Optimal transport in Brownian motion stopping

  • Young-Heon Kim (University of British Columbia)
Live Stream

Abstract

We consider an optimal transport problem arising from stopping the Brownian motion from a given distribution to get a fixed or free target distribution; the fixed target case is often called the optimal Skorokhod embedding problem in the literature, a popular topic in math finance pioneered by many people. Our focus is on the case of general dimensions, which has not been well understood. We explain that under certain natural assumptions on the transportation cost, the optimal stopping time is given by the hitting time to a barrier, which is determined by the solution to the dual optimization problem. In the free target case, the problem is related to the Stefan problem, that is, a free boundary problem for the heat equation. We obtain analytical information on the optimal solutions, including certain BV estimates. The fixed target case is mainly from the joint work with Nassif Ghoussoub and Aaron Palmer at UBC, while the free target case is the recent joint work (in-progress) with Inwon Kim at UCLA.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
  • Mar 26, 2024 tba with Phan Thành Nam
  • Mar 26, 2024 tba with Dominik Schmid
  • May 7, 2024 tba with Manuel Gnann
  • May 14, 2024 tba with Barbara Verfürth
  • May 14, 2024 tba with Lisa Hartung
  • Jun 25, 2024 tba with Paul Dario
  • Jul 16, 2024 tba with Michael Loss