  The inf-convolution of risk measures is directly related to risk sharing and
general equilibrium, and it has attracted considerable attention in
mathematical finance and insurance problems. However, the theory is restricted
to finite sets of risk measures. This study extends the inf-convolution of risk
measures in its convex-combination form to a countable (not necessarily finite)
set of alternatives. The intuitive meaning of this approach is to represent a
generalization of the current finite convex weights to the countable case.
Subsequently, we extensively generalize known properties and results to this
framework. Specifically, we investigate the preservation of properties, dual
representations, optimal allocations, and self-convolution.
