Conditional Mean Risk Sharing of Independent Discrete Losses in Large Pools

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

No 2024022, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: This paper considers a risk sharing scheme of independent discrete losses that combines risk retention at individual level, risk transfer for too expensive losses and risk pooling for the middle layer. This ensures that pooled losses can be considered as being uniformly bounded. We study the no-sabotage requirement and diversification effects when the conditional mean risk-sharing rule is applied to allocate pooled losses. The no-sabotage requirement is equivalent to Efron’s monotonicity property for conditional expectations, which is known to hold under log-concavity. Elementary proofs of this result for discrete losses are provided for finite population pools. The no-sabotage requirement and diversification effects are then examined within large pools. It is shown that Efron’s monotonicity property holds asymptotically and that risk can be eliminated under fairly general conditions which are fulfilled in applications.

Keywords: Risk pooling; Peer-to-Peer (P2P) insurance; Conditional mean risk-sharing; Likelihood ratio order; Log-concavity (search for similar items in EconPapers)
Pages: 22
Date: 2024-09-16
Note: In: Methodology and Computing in Applied Probability, 2024, vol. 26, 36
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2024022

DOI: 10.1007/s11009-024-10106-w

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