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Mixed Poisson process with Pareto mixing variable and its risk applications∗

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Abstract

This paper considers a mixed Poisson process with Pareto mixing variable, Exp-Pareto, and Erlang–Pareto distributions. New important properties of these distributions are derived.Approximations of the random time transformed Cramér–Lundberg collective risk model with Pareto mixing variable and different claim sizes, with finite or infinite means are given. The resulting risk model has dependent, Exp-Pareto interarrival times with Archimedean copulas.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Shumen University, Universitetska str. 115, 9700, Shumen, Bulgaria

    Pavlina Jordanova

  2. Institute of Statistics, Valparaiso University, Valparaíso, Chile

    Milan Stehlík

  3. Department of Applied Statistics, Johannes Kepler University, Altenbergerstrasse 69, 4040, Linz, Austria

    Milan Stehlík

Authors
  1. Pavlina Jordanova
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  2. Milan Stehlík
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Correspondence to Pavlina Jordanova.

Additional information

*This work is partially supported by project Fondecyt Proyecto Regular No. 1151441.

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Jordanova, P., Stehlík, M. Mixed Poisson process with Pareto mixing variable and its risk applications∗ . Lith Math J 56, 189–206 (2016). https://doi.org/10.1007/s10986-016-9313-4

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  • DOI: https://doi.org/10.1007/s10986-016-9313-4

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