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

Ehyter Matías Martín-González (), Ekaterina Todorova Kolkovska () and Antonio Murillo-Salas ()
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Ehyter Matías Martín-González: Universidad de Guanajuato
Ekaterina Todorova Kolkovska: Centro de Investigación en Matemáticas
Antonio Murillo-Salas: Universidad de Guanajuato

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 3, 753-766

Abstract: 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.

Keywords: Extreme value theory; Pareto tail; Integrated tail; Equilibrium distribution; Classical risk process; Estimated ruin probability; 62E20; 62P05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11009-020-09779-w

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