Seminar by Cagin Ararat (USC and Bilkent U)

Event Date: 

Monday, May 15, 2023 - 3:30pm to 4:30pm

Event Location: 

  • Sobel room (SH 5607F)

Seminar by Prof. Cagin Ararat,  Assistant Professor,  Department of Industrial Engineering, Bilkent University

During 2022-23: Visiting Fulbright ScholarDepartment of Mathematics, University of Southern California

Title: Set-valued martingales and backward stochastic differential equations

Abstract: Motivated by the connection between univariate dynamic risk measures and backward stochastic differential equations, we start building a theory for set-valued backward stochastic differential equations (SV-BSDE). As a first step for this purpose, we formulate a simple SV-BSDE with a compact-valued driver function and study the well-posedness of this SV-BSDE. A key tool in establishing well-posedness is the availability of a stochastic integral representation for set-valued martingales. We prove a new martingale representation theorem which, in contrast to the available literature, allows the initial value of the martingale to be nontrivial. This is a joint work with Jin Ma and Wenqian Wu.

Assistant Professor, currently on sabbatical leave

Department of Industrial Engineering, Bilkent University

Visiting Fulbright Scholar

Department of Mathematics, University of Southern California