Set-valued Ito's formula with an application to the general set-valued backward stochastic differential equation

Abstract: The overarching goal of this paper is to establish a set-valued It^{o}'s formula. As an application, we obtain the existence and uniqueness of solutions for the general set-valued backward stochastic differential equation which gives an answer to an open question proposed by Ararat et al. (C. Ararat, J. Ma and W.Q. Wu, Set-valued backward stochastic differential equation, arXiv:2007.15073).