Explore a comprehensive lecture on set-valued martingales and backward stochastic differential equations (SV-BSDE) presented by Çağın Ararat from Bilkent University. Delve into the theory behind SV-BSDEs, motivated by the connection between univariate dynamic risk measures and backward stochastic differential equations. Examine the formulation of a simple SV-BSDE with a compact-valued driver function and investigate its well-posedness. Discover a key tool in establishing well-posedness through the availability of a stochastic integral representation for set-valued martingales. Learn about a new martingale representation theorem that allows for nontrivial initial values, contrasting with existing literature. Gain insights into this joint work with Jin Ma and Wenqian Wu, presented as part of the USC Probability and Statistics Seminar.