Inf-convolution and optimal risk sharing with countable sets of risk measures

Abstract: 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.