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A Multinomial Approximation Approach for the Finite Time Survival Probability Under the Markov-modulated Risk Model |
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| Authors: | Li Jingchao Su Bihao Wei Zhenghong Nie Ciyu |
| Affiliation: | 1.College of Mathematics and Statistics, Shenzhen University, Nanhai Ave 3688, Shenzhen, Guangdong, 518060, P.R. China ;2.Shenzhen Key Laboratory of Advanced Machine Learning and Applications, Shenzhen University, Shenzhen, 518060, Guangdong, P.R. China ;3.School of Mathematics, Shanghai University of Finance and Economics, 200433, Shanghai, China ;4.Division of Banking and Finance, Nanyang Business School, Nanyang Technological University, 50 Nanyang Avenue, Nanyang, 639798, Singapore ; |
| 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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