Ranking the extreme claim amounts in dependent individual risk models

Nuria Torrado and Jorge Navarro

Scandinavian Actuarial Journal, 2021, vol. 2021, issue 3, 218-247

Abstract: In risk theory, the distribution of extreme claim amounts of dependent risks is an essential element, since it provides valuable information to companies for developing risk reduction strategies. In this article, we obtain a representation of the distributions of the smallest and the largest claim amounts based on a new concept of semi-distorted distribution. This concept extends the well known concept of distorted distributions introduced previously in risk theory. Based on this representation, we obtain distribution-free comparisons between extreme claim amounts in the sense of different stochastic dominances when the risks have a fixed dependence structure. Several examples illustrate the application of the theoretical results.

Date: 2021
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DOI: 10.1080/03461238.2020.1830845

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