Our speaker is Valentin Tissot-Daguette, PhD candidate in Operations Research and Financial Engineering at Princeton.

Abstract: An Itô calculus is developed for functionals of  the "time" spent by a path at arbitrary levels. We recover a Markovian setting by lifting a process with its flow of occupation measures, and call the resulting pair the occupied process. As the occupation measure erases the chronology of the path, the study of occupied processes strikes a middle ground between the classical Itô calculus and the fully path-dependent case pioneered by Dupire. We extend Itô's and Feynman-Kac’s formula after introducing the occupation derivative, a projection of the linear derivative popularized in mean field games and McKean-Vlasov control problems. Through Feynman-Kac, a large class of path-dependent PDEs are conveniently recast as parabolic problems where the occupation measure plays the role of time. Financial examples are finally discussed.