Monotonicity results for portfolios with heterogeneous claims arrival processes

Esther Frostig; Michel Denuit

doi:10.1016/j.insmatheco.2005.11.007

Monotonicity results for portfolios with heterogeneous claims arrival processes

Esther Frostig, Michel Denuit

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Loosely speaking, actuaries believe that the heterogeneity of the risks tends to increase dangerousness. This in turn leads to requiring more economic capital. This paper aims to formalize this intuitive idea. More specifically, vectors of compound sums will be considered, with different claim frequency distributions and/or different claim severity distributions. The effect of increasing the heterogeneity will be studied with the help of majorization. Various multivariate integral stochastic orderings will be used to compare situations according to their level of heterogeneity.

Original language	English
Pages (from-to)	484-494
Number of pages	11
Journal	Insurance: Mathematics and Economics
Volume	38
Issue number	3
DOIs	https://doi.org/10.1016/j.insmatheco.2005.11.007
State	Published - 15 Jun 2006

Bibliographical note

Funding Information:
Michel Denuit acknowledges the financial support of the C ommunauté française de Belgique under contract “Projet d’Actions de Recherche Concertées” ARC 04/09-320, as well as the financial support of the Banque Nationale de Belgique under grant “Risk measures and Economic capital”.

Keywords

Majorization
Risk measures
Schur-increasingness
Univariate and multivariate stochastic orders

ASJC Scopus subject areas

Statistics and Probability
Economics and Econometrics
Statistics, Probability and Uncertainty

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10.1016/j.insmatheco.2005.11.007

Cite this

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abstract = "Loosely speaking, actuaries believe that the heterogeneity of the risks tends to increase dangerousness. This in turn leads to requiring more economic capital. This paper aims to formalize this intuitive idea. More specifically, vectors of compound sums will be considered, with different claim frequency distributions and/or different claim severity distributions. The effect of increasing the heterogeneity will be studied with the help of majorization. Various multivariate integral stochastic orderings will be used to compare situations according to their level of heterogeneity.",

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AB - Loosely speaking, actuaries believe that the heterogeneity of the risks tends to increase dangerousness. This in turn leads to requiring more economic capital. This paper aims to formalize this intuitive idea. More specifically, vectors of compound sums will be considered, with different claim frequency distributions and/or different claim severity distributions. The effect of increasing the heterogeneity will be studied with the help of majorization. Various multivariate integral stochastic orderings will be used to compare situations according to their level of heterogeneity.

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KW - Univariate and multivariate stochastic orders

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ER -

Monotonicity results for portfolios with heterogeneous claims arrival processes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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