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

Marcelo Righi () and Marlon Ruoso Moresco ()
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Marlon Ruoso Moresco: Federal University of Rio Grande do Sul

Annals of Operations Research, 2024, vol. 336, issue 1, No 27, 829-860

Abstract: 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.

Keywords: Risk measures; Inf-convolution; Risk sharing; Representations; Optimal allocations (search for similar items in EconPapers)
Date: 2024
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Working Paper: Inf-convolution and optimal risk sharing with countable sets of risk measures (2022)
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DOI: 10.1007/s10479-022-04593-8

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