Banach Contraction Principle and ruin probabilities in regime-switching models
Lesław Gajek and
Insurance: Mathematics and Economics, 2018, vol. 80, issue C, 45-53
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)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:80:y:2018:i:c:p:45-53
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