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Approximation of the Equilibrium Distribution via Extreme Value Theory: an Application to Insurance Risk

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Abstract

We use the excess over a threshold method (see e.g. Embrechts et al. 1997) to approximate the tails of equilibrium distributions (integrated tail distributions) associated to distributions with regularly varying tail. We evaluate the performance of our approximations in some particular cases of distributions with regularly varying tails. Finally, we apply our results to the Danish reinsurance real data set.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Guanajuato, Guanajuato, Mexico

    Ehyter Matías Martín-González & Antonio Murillo-Salas

  2. Área de Probabilidad y Estadística, Centro de Investigación en Matemáticas, Guanajuato, Mexico

    Ekaterina Todorova Kolkovska

Authors
  1. Ehyter Matías Martín-González
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  2. Ekaterina Todorova Kolkovska
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  3. Antonio Murillo-Salas
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Correspondence to Ehyter Matías Martín-González.

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Ehyter Matías Martín-González research was supported by PRODEP-UG, grant F-PROMEP-38/Rev-04.

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Martín-González, E.M., Kolkovska, E.T. & Murillo-Salas, A. Approximation of the Equilibrium Distribution via Extreme Value Theory: an Application to Insurance Risk. Methodol Comput Appl Probab 23, 753–766 (2021). https://doi.org/10.1007/s11009-020-09779-w

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  • DOI: https://doi.org/10.1007/s11009-020-09779-w

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