121 citations · 301 across the 31 of their papers we have counts for
4 papers · 1 filter
Capacities, Measurable Selection and Dynamic Programming Part I: Abstract Framework
Nicole El Karoui, Xiaolu Tan
We give a brief presentation of the capacity theory and show how it derives naturally a measurable selection theorem following the approach of Dellacherie (1972). Then we present t…
Optimal transportation under controlled stochastic dynamics
Xiaolu Tan, Nizar Touzi
We consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends…
Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems
Nicole El Karoui, Xiaolu Tan
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By c…
Weak approximation of second-order BSDEs
Dylan Possamaï, Xiaolu Tan
We study the weak approximation of the second-order backward SDEs (2BSDEs), when the continuous driving martingales are approximated by discrete time martingales. We establish a co…