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Inf-convolution and optimal risk sharing with countable sets of risk measures
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. In this study, we extend the inf-convolution
of risk measures in its convex-combination form to a countable (not necessarily
finite) set of alternatives. The intuitive principle of this approach a
generalization of convex weights in the finite 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