  In this paper, we introduce a new class of set-valued risk measures, named
set-valued star-shaped risk measures. Motivated by the results of scalar
monetary and star-shaped risk measures, this paper investigates the
representation theorems in the set-valued framework. It is demonstrated that
set-valued risk measures can be represented as the union of a family of
set-valued convex risk measures, and set-valued normalized star-shaped risk
measures can be represented as the union of a family of set-valued normalized
convex risk measures. The link between set-valued risk measures and set-valued
star-shaped risk measures is also established.
