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.