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Risks 2018, 6(3), 91; https://doi.org/10.3390/risks6030091

The Stability of the Aggregate Loss Distribution

Institute of Mathematical Statistics and Actuarial Science, Department of Mathematics and Statistics, University of Bern, 3012 Bern, Switzerland
Received: 17 August 2018 / Revised: 31 August 2018 / Accepted: 4 September 2018 / Published: 5 September 2018
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Abstract

In this article we introduce the stability analysis of a compound sum: it consists of computing the standardized variation of the survival function of the sum resulting from an infinitesimal perturbation of the common distribution of the summands. Stability analysis is complementary to the classical sensitivity analysis, which consists of computing the derivative of an important indicator of the model, with respect to a model parameter. We obtain a computational formula for this stability from the saddlepoint approximation. We apply the formula to the compound Poisson insurer loss with gamma individual claim amounts and to the compound geometric loss with Weibull individual claim amounts. View Full-Text
Keywords: Dirac distribution; gamma-Poisson; Weibull-geometric compound distributions; Gâteaux differential; saddlepoint approximation Dirac distribution; gamma-Poisson; Weibull-geometric compound distributions; Gâteaux differential; saddlepoint approximation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Gatto, R. The Stability of the Aggregate Loss Distribution. Risks 2018, 6, 91.

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