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Banach Contraction Principle and ruin probabilities in regime-switching models

Lesław Gajek and Marcin Rudź

Insurance: Mathematics and Economics, 2018, vol. 80, issue C, 45-53

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.

Keywords: Risk operators; Banach Contraction Principle; Regime-switching models; Ruin probabilities; Markov chains (search for similar items in EconPapers)
Date: 2018
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Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

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