Finite-Horizon Ruin Probabilities in a Risk-Switching Sparre Andersen Model

  • Lesław Gajek
  • Marcin Rudź
Open Access


After implementation of Solvency II, insurance companies can use internal risk models. In this paper, we show how to calculate finite-horizon ruin probabilities and prove for them new upper and lower bounds in a risk-switching Sparre Andersen model. Due to its flexibility, the model can be helpful for calculating some regulatory capital requirements. The model generalizes several discrete time- as well as continuous time risk models. A Markov chain is used as a ‘switch’ changing the amount and/or respective wait time distributions of claims while the insurer can adapt the premiums in response. The envelopes of generalized moment generating functions are applied to bound insurer’s ruin probabilities.


Risk operators Risk-switching models Ruin probabilities Mgf’s envelopes Risk management based on internal models Solvency II 

Mathematics Subject Classification (2010)

91B30 60J20 60J22 



The authors thank the reviewers and the editors for helpful comments.


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Copyright information

© The Author(s) 2018

Open AccessThis 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.Institute of Mathematics Lodz University of TechnologyŁódźPoland
  2. 2.Polish Financial Supervision AuthorityWarszawaPoland

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