Large-Loss Behavior of Conditional Mean Risk Sharing

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.

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Document type	Article de périodique (Journal article) – Article de recherche
Access type	Accès restreint
Publication date	2020
Language	Anglais
Journal information	"ASTIN Bulletin" - Vol. 50, no.3, p. 1093-1122 (2020)
Peer reviewed	yes
Publisher	Cambridge University Press (CUP)
issn	0515-0361
e-issn	1783-1350
Publication status	Publié
Affiliation	UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Keywords	Conditional expectation ; risk pooling ; compound distributions ; Panjer formula ; size-biased transform
Links	https://www.cambridge.org/core/journals/astin-bulletin-journal-of-the-iaa/article/largeloss-behavior-of-conditional-mean-risk-sharing/B6AE93167BC6BD47C35BB050C292B05F https://doi.org/10.1017/asb.2020.23[DOI] http://hdl.handle.net/2078.1/235799[Handle]

See also
	[boreal:230339]	Ultimate behavior of conditional mean risk sharing for independent compound Panjer-Katz sums with gamma and Pareto severities