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. Joint work with Jin Ma and Wenqian Wu.
Bio: Çağın Ararat is an Assistant Professor in the Department of Industrial Engineering at Bilkent University. He received his BSc degree in 2010 from the same department, followed by a PhD degree in 2015 from ORFE. His research interests include risk measures, systemic risk, set-valued stochastic analysis and backward stochastic differential equations. During the academic year 2022-2023, he is on sabbatical leave and visiting the Department of Mathematics at the University of Southern California as a Fulbright Scholar.