Large-Loss Behavior of Conditional Mean Risk Sharing

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

No 2020021, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: We consider the conditional mean risk allocation for an insurance pool, as defined by Denuit and Dhaene (2012). Precisely, we study the asymptotic behavior of the respective relative contributions of the participants as the total loss of the pool tends to infinity. The numerical illustration in Denuit (2019) suggests that the application of the conditional mean risk sharing rule may produce a linear sharing in the tail of the total loss distribution. This paper studies the validity of this empirical finding in the class of compound Panjer–Katz sums consisting of compound Binomial, compound Poisson, and compound Negative Binomial sums with either Gamma or Pareto severities. It is demonstrated that such a behavior does not hold in general since one term may dominate the other ones conditional of large total loss.

Keywords: Conditional expectation; risk pooling; compound distributions; Panjer formula; size-biased transform (search for similar items in EconPapers)
Date: 2020-07-13
Note: In: ASTIN Bulletin - Vol. 50, no.3, p. 1093-1122 (2020)
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2020021

DOI: 10.1017/asb.2020.23

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