Asymptotics and Approximations of Ruin Probabilities for Multivariate Risk Processes in a Markovian Environment

  • G. A. DelsingEmail author
  • M. R. H. Mandjes
  • P. J. C. Spreij
  • E. M. M. Winands
Open Access


This paper develops asymptotics and approximations for ruin probabilities in a multivariate risk setting. We consider a model in which the individual reserve processes are driven by a common Markovian environmental process. We subsequently consider a regime in which the claim arrival intensity and transition rates of the environmental process are jointly sped up, and one in which there is (with overwhelming probability) maximally one transition of the environmental process in the time interval considered. The approximations are extensively tested in a series of numerical experiments.


Ruin probability Insurance risk Markov processes Approximations Multi-dimensional risk process 

Mathematics Subject Classification (2010)




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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Korteweg-de Vries InstituteUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.RabobankUtrechtThe Netherlands
  3. 3.CWIAmsterdamThe Netherlands
  4. 4.Radboud UniversityNijmegenThe Netherlands

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