Conditional mean risk sharing in the individual model with graphical dependencies

Michel Denuit and Christian Y. Robert
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Michel Denuit: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2022020, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: Conditional mean risk sharing appears to be effective to distribute total losses amongst participants within an insurance pool. This paper develops analytical results for this allocation rule in the individual risk model with dependence induced by the respective position within a graph. Precisely, losses are modelled by zero-augmented random variables whose joint occurrence distribution and individual claim amount distributions are based on network structures and can be characterised by graphical models. The Ising model is adopted for occurrences and loss amounts obey decomposable graphical models that are specific to each participant. Two graphical structures are thus used: the first one to describe the contagion amongst member units within the insurance pool and the second one to model the spread of losses inside each participating unit. The proposed individual risk model is typically useful for modelling operational risks, catastrophic risks or cybersecurity risks.

Keywords: Graphical models; Ising model; decomposable graphs; size-biased transform (search for similar items in EconPapers)
JEL-codes: G22 (search for similar items in EconPapers)
Pages: 27
Date: 2022-01-01
Note: In: Annals of Actuarial Science, 2022, vol. 16(1), p. 183-209
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2022020

DOI: 10.1017/S1748499521000166

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