  We study combinations of risk measures under no restrictive assumption on the
set of alternatives. We develop and discuss results regarding the preservation
of properties and acceptance sets for the combinations of risk measures. One of
the main results is the representation of resulting risk measures from the
properties of both alternative functionals and combination functions. We build
on developing a dual representation for an arbitrary mixture of convex risk
measures. In this case, we obtain a penalty that recalls the notion of
inf-convolution under theoretical measure integration. We develop results
related to this specific context. We also explore features of individual
interest generated by our frameworks, such as the preservation of continuity
properties and the representation of worst-case risk measures.
