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A generalization of Gerber’s inequality for ruin probabilities in risk-switching models

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  • Gajek, Lesław
  • Rudź, Marcin

Abstract

In this paper, we investigate a risk-switching Sparre Andersen model which generalizes several discrete time- as well as continuous time risk models. A Markov chain is used as a ‘switch’ under the assumption that jumps change the amount and/or respective wait time distributions of claims while the insurer can adapt the premiums in response. A generalized Gerber-type inequality for the vector of ruin probabilities is proven showing that the risk-switching models allow sophisticated mathematical results in spite of their complexity.

Suggested Citation

  • Gajek, Lesław & Rudź, Marcin, 2017. "A generalization of Gerber’s inequality for ruin probabilities in risk-switching models," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 236-240.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:236-240
    DOI: 10.1016/j.spl.2017.06.001
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    References listed on IDEAS

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    Cited by:

    1. Gajek, Lesław & Rudź, Marcin, 2018. "Banach Contraction Principle and ruin probabilities in regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 45-53.

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