Publication date: Available online 4 March 2018
Source:Insurance: Mathematics and Economics
Author(s): Lesław Gajek, Marcin Rudź
We apply Banach Contraction Principle to approximate a vector 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 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 and control the error of approximation. Numerical examples confirm high accuracy of the resulting procedure.
Source:Insurance: Mathematics and Economics
Author(s): Lesław Gajek, Marcin Rudź