Abstract
In this paper, we consider the problem of computing different types of finite time survival probabilities for a Markov-Modulated risk model and a Markov-Modulated risk model with reinsurance, both with varying premium rates. We use the multinomial approximation scheme to derive an efficient recursive algorithm to compute finite time survival probabilities and finite time draw-down survival probabilities. Numerical results show that by comparing with MCMC approximation, discretize approximation and diffusion approximation methods, the proposed scheme performs accurate results in all the considered cases and with better computation efficiency.
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Acknowledgements
The authors are most grateful to referees for their very thorough reading of the paper and valuable suggestions. The research of Jingchao Li was supported by the National Key R&D Program of China (Grant No. 2020YFB2103503 ), the National Natural Science Foundation of China (project No. 11601344), Shenzhen peacock program (project No. 000417), Natural Science Foundation of Guangdong Province (project No. 2020A1515010372), the Humanities and Social Sciences Project of the Ministry Education of China (No. 19YJA910002), the Natural Science Foundation of Shandong Province (No. ZR2018MG002). The authors wish to express their gratitude for these financial supports.
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Li, J., Su, B., Wei, Z. et al. A Multinomial Approximation Approach for the Finite Time Survival Probability Under the Markov-modulated Risk Model. Methodol Comput Appl Probab 24, 2169–2194 (2022). https://doi.org/10.1007/s11009-021-09897-z
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DOI: https://doi.org/10.1007/s11009-021-09897-z