Details

Autor(en) / Beteiligte

• Liu, Yuxuan
• Jiang, Zhengjun
• Zhang, Yiwen

Titel

q-scale function, Banach contraction principle, and ultimate ruin probability in a Markov-modulated jump-diffusion risk model

Ist Teil von

• Scandinavian actuarial journal, 2023-01, Vol.2023 (1), p.38-50

Ort / Verlag

Stockholm: Taylor & Francis

Erscheinungsjahr

2023

Link zum Volltext

Quelle

EBSCOhost Business Source Ultimate

Beschreibungen/Notizen

• The paper investigates ultimate ruin probability, the probability that ruin time is finite, for an insurance company whose risk reserves follow a Markov-modulated jump-diffusion risk model. We use both the Banach contraction principle and q-scale functions to prove that ultimate ruin probability is the only fixed point of a contraction mapping and show that an iterative equation can be employed to calculate ultimate ruin probability by an iterative algorithm of approximating the fixed point. Using q-scale functions and the methodology from Gajek and Rudź [(2018). Banach contraction principle and ruin probabilities in regime-switching models. Insurance: Mathematics and Economics, 80, 45-53] applied to the Markov-modulated jump-diffusion risk model, we get a more explicit Lipschitz constant in the Banach contraction principle and conveniently verify some similar results of their appendix in our case.