SIZE-BIASED TRANSFORM AND CONDITIONAL MEAN RISK SHARING, WITH APPLICATION TO P2P INSURANCE AND TONTINES
By Michel Denuit. ASTIN Bulletin: The Journal of the International Actuarial Association, 2019
59 citations recorded by the source corpus.
Abstract Using risk-reducing properties of conditional expectations with respect to convex order, Denuit and Dhaene [Denuit, M. and Dhaene, J. (2012). Insurance: Mathematics and Economics 51, 265–270] proposed the conditional mean risk sharing rule to allocate the total risk among participants to an insurance pool. This paper relates the conditional mean risk sharing rule to the size-biased transform when pooled risks are independent. A representation formula is first derived for the conditional expectation of an individual risk given the aggregate loss. This formula is then exploited to obtain explicit expressions for the contributions to the pool when losses are modeled by compound Poisson sums, compound Negative Binomial sums, and compound Binomial sums, to which Panjer recursion applies. Simple formulas are obtained when claim severities are homogeneous. A couple of applications are considered: first, to a peer-to-peer insurance scheme where participants share the first layer of their respective risks while the higher layer is ceded to a (re)insurer; second, to survivor credits to be shared among surviving participants in tontine schemes.
Subfields: Demography, Economics and Econometrics, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/cf38c389e415412bd8aa1af0f3e8abbc7f97b47c
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Citations in the corpus
- From risk sharing to pure premium for a large number of heterogeneous losses (2021, methodology): “The properties of this scheme have been studied in Denuit (2019) and Denuit and Robert (2020) when the number of participants is fixed.”