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On the spectral properties and convergence of the bonus-malus Markov chain model | ||
| Journal of Mathematical Modeling | ||
| مقاله 17، دوره 9، شماره 4، اسفند 2021، صفحه 573-583 اصل مقاله (308.42 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2021.18991.1625 | ||
| نویسنده | ||
| Kenichi Hirose* | ||
| 10-17 Moto-machi, Ono City, Fukui 912-0081, Japan | ||
| چکیده | ||
| In this paper, we study the bonus-malus model denoted by $BM_k (n)$. It is an irreducible and aperiodic finite Markov chain but it is not reversible in general. We show that if an irreducible, aperiodic finite Markov chain has a transition matrix whose secondary part is represented by a nonnegative, irreducible and periodic matrix, then we can estimate an explicit upper bound of the coefficient of the leading-order term of the convergence bound. We then show that the $BM_k (n)$ model has the above-mentioned periodicity property. We also determine the characteristic polynomial of its transition matrix. By combining these results with a previously studied one, we obtain essentially complete knowledge on the convergence of the $BM_k (n)$ model in terms of its stationary distribution, the order of convergence, and an upper bound of the coefficient of the convergence bound. | ||
| کلیدواژه‌ها | ||
| Bonus-malus system؛ Markov chains؛ convergence to stationary distribution؛ the Perron-Frobenius theorem | ||
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آمار تعداد مشاهده مقاله: 704 تعداد دریافت فایل اصل مقاله: 635 |
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