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Banach Contraction Principle and ruin probabilities in regime-switching models

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  • Gajek, Lesław
  • Rudź, Marcin

Abstract

We apply Banach Contraction Principle to approximate a vector Ψ of ruin probabilities in regime-switching models. A Markov chain is interpreted as a ‘switch’ that changes the amount and/or wait time distributions of claims. The insurer has a possibility to adapt the premium rates in response. An associated risk operator L is proven to be a contraction on a properly chosen complete metric space while Ψ is shown to be the unique fixed point of L within this space. Thus, by iterating L on any of its points, we can simultaneously approximate Ψ and control the error of approximation. Numerical examples confirm high accuracy of the resulting procedure.

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  • 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.
    • Handle: RePEc:eee:insuma:v:80:y:2018:i:c:p:45-53
    DOI: 10.1016/j.insmatheco.2018.02.005
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    References listed on IDEAS

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    1. 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.
    2. Lesław Gajek & Marcin Rudź, 2018. "Risk-switching insolvency models," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 51, pages 129-146.

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