On a family of risk measures based on largest claims

  1. Antonia Castaño 1
  2. Gema Pigueiras 1
  3. Miguel Ángel Sordo 1
  1. 1 Department of Statistics and Operation Research, University of Cádiz, Spain
Actas:
18th Applied Stochastic Models and Data Analysis International Conference

Editorial: ISAST: International Society for the Advancement of Science and Technology

ISBN: 978-618-5180-32-4

Año de publicación: 2019

Páginas: 48

Tipo: Aportación congreso

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Resumen

In an insurance framework, we introduce a family of premium principles in terms of the expected average risk of the largest claims in a set of independent and identically distributed claims. Each premium principle of this family can be represented by mixtures of tail value-at-risks, with beta mixing distributions. From this representation, we obtain a convergence result that connects the tail value-at-risk with the largest claims of aportfolio. A characterization of the excess-wealth order in terms of this family of premiums is provided. As a consequence, we obtain a sufficientcondition for ordering the net premiums of two collective risks under the ECOMOR reinsurance treaty.