Investigates ruin probabilities in an insurance company's risk model, suggesting effective numerical methods for risk assessment.
The paper studies ultimate ruin probability that ruin time is finite for an insurance company with its risk reserves governed by a Markov-modulated jump-diffusion risk model with double-exponential jumps. By using q-scale function and the method of Gajek and Rudź [(2018) Banach contraction principle and ruin probabilities in regime-switching models. Insurance: Mathematics and Economics, 80, 45–53], the paper confirms that the ultimate ruin probability is indeed the unique fixed point of a contraction mapping with a closed-form Lipschitz constant and can be approximated via an iterative equation. Finally, we use a three-regime numerical example to show how to get regime-switching ruin probabilities by using numerical q-scale functions and the iterative algorithm in MATLAB, compare the iterative results with Monte Carlo simulations as a cross-validation, and then conduct a sensitivity analysis of regime-switching ruin probabilities to every parameter.
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Bu et al. (2026) studied this question.
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