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

Author

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  • Lesław Gajek

    (Institute of Mathematics Lodz University of Technology
    Polish Financial Supervision Authority)

  • Marcin Rudź

    (Institute of Mathematics Lodz University of Technology)

Abstract

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.

Suggested Citation

  • Lesław Gajek & Marcin Rudź, 2020. "Finite-Horizon Ruin Probabilities in a Risk-Switching Sparre Andersen Model," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1493-1506, December.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:4:d:10.1007_s11009-018-9627-2
    DOI: 10.1007/s11009-018-9627-2
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    References listed on IDEAS

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