Polynomial series expansions and moment approximations for conditional mean risk sharing of insurance losses

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

No 2021016, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: This paper exploits the representation of the conditional mean risk sharing allocations in terms of size-biased transforms to derive effective approximations within insurance pools of limited size. Precisely, the probability density functions involved in this representation are expanded with respect to the Gamma density and its associated Laguerre orthonormal polynomials, or with respect to the Normal density and its associated Hermite polynomials when the size of the pool gets larger. Depending on the thickness of the tails of the loss distributions, the latter may be replaced with their Esscher transform (or exponential tilting) of negative order. The numerical method then consists in truncating the series expansions to a limited number of terms. This results in an approximation in terms of the first moments of the individual loss distributions. Compound Panjer-Katz sums are considered as an application. The proposed method is compared with the well-established Panjer recursive algorithm. It appears to provide the analyst with reliable approximations that can be used to tune system parameters, before performing exact calculations.

Keywords: conditional expectation; size-biased transform; Esscher transform; exponential tilting; Laguerre polynomials; Hermite polynomials (search for similar items in EconPapers)
Pages: 19
Date: 2021-03-16
New Economics Papers: this item is included in nep-ias, nep-ore and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://dial.uclouvain.be/pr/boreal/fr/object/bore ... tastream/PDF_01/view (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvad:2021016

Access Statistics for this paper

More papers in LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA) Voie du Roman Pays 20, 1348 Louvain-la-Neuve (Belgium). Contact information at EDIRC.
Bibliographic data for series maintained by Nadja Peiffer ().