  In this paper, we mainly focus on the set-valued (stochastic) analysis on the
space of convex, closed, but possibly unbounded sets, and try to establish a
useful theoretical framework for studying the set-valued stochastic
differential equations with unbounded coefficients. The space that we will be
focusing on are convex, closed sets that are "generated" by a given cone, in
the sense that the Hausdorff distance of all elements to the "generating" cone
is finite. Such space should in particular include the so-called "upper sets",
and has many useful cases in finance, such as the well-known set-valued risk
measures, as well as the solvency cone in some super-hedging problems. We shall
argue that, for such a special class of unbounded sets, under some conditions,
the cancellation law is still valid, eliminating a major obstacle for extending
the set-valued analysis to non-compact sets. We shall establish some basic
algebraic and topological properties of such spaces, and show that some
standard techniques will again be valid in studying the set-valued SDEs with
unbounded (drift) coefficients which, to the best of our knowledge, is new.
