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Schur-Constant and Related Dependence Models, with Application to Ruin Probabilities

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Abstract

This paper relates to Schur-constant vectors in their usual continuous version. Our first goal is to highlight the existing links with L1 symmetric Dirichlet vectors and Archimedean copulas. This leads us to briefly review the main properties of these three dependency models. Several special cases, mostly classical, are also examined in this context. Next, a discrete time risk model is considered in which the successive claims amounts constitute a Schur-constant vector. A simple compact formula is obtained for the corresponding probabilities of ruin. Its application is illustrated by some numerical examples.

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Acknowledgements

We are grateful to the editors and the referees for useful comments and suggestions. C. Lefèvre received the support of the Chair DIALog sponsored by CNP Assurances. M. Simon received the support from ACEMS, the Australian Research Council Center of Excellence for Mathematical and Statistical Frontiers.

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Authors and Affiliations

  1. Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, B-1050, Bruxelles, Belgium

    Claude Lefèvre

  2. School of Mathematics and Statistics, University of Melbourne, Parkville, VIC, 3010, Australia

    Matthieu Simon

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  1. Claude Lefèvre
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  2. Matthieu Simon
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Correspondence to Claude Lefèvre.

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Lefèvre, C., Simon, M. Schur-Constant and Related Dependence Models, with Application to Ruin Probabilities. Methodol Comput Appl Probab 23, 317–339 (2021). https://doi.org/10.1007/s11009-019-09744-2

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  • DOI: https://doi.org/10.1007/s11009-019-09744-2

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