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

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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.

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Authors and Affiliations

  1. Business School, Federal University of Rio Grande do Sul, Washington Luiz, 855, Porto Alegre, 90010-460, Brazil

    Marcelo Brutti Righi & Marlon Ruoso Moresco

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  1. Marcelo Brutti Righi
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  2. Marlon Ruoso Moresco
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Correspondence to Marcelo Brutti Righi.

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We thank the Lead Guest Editor, Professor Claudio Fontana, and the two anonymous Reviewers for their constructive comments, which have been useful to improve both the technical quality and presentation of the manuscript. We are grateful for the financial support of FAPERGS (Rio Grande do Sul State Research Council) project number 17/2551-0000862-6 and CNPq (Brazilian Research Council) projects number 302369/2018-0 and 407556/2018-4.

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Righi, M.B., Moresco, M.R. Inf-convolution and optimal risk sharing with countable sets of risk measures. Ann Oper Res 336, 829–860 (2024). https://doi.org/10.1007/s10479-022-04593-8

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