Asymptotics and Approximations of Ruin Probabilities for Multivariate Risk Processes in a Markovian Environment
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DOI: 10.1007/s11009-019-09742-4
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- D. Anderson & J. Blom & M. Mandjes & H. Thorsdottir & K. Turck, 2016. "A Functional Central Limit Theorem for a Markov-Modulated Infinite-Server Queue," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 153-168, March.
- Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
- Philippe Picard & Claude Lefèvre & Ibrahim Coulibaly, 2003. "Multirisks Model and Finite-Time Ruin Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 5(3), pages 337-353, September.
- Jun Cai & David Landriault & Tianxiang Shi & Wei Wei, 2017. "Joint Insolvency Analysis of a Shared MAP Risk Process: A Capital Allocation Application," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(2), pages 178-192, April.
- Cai, Jun & Li, Haijun, 2007. "Dependence properties and bounds for ruin probabilities in multivariate compound risk models," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 757-773, April.
- Avram, Florin & Palmowski, Zbigniew & Pistorius, Martijn, 2008. "A two-dimensional ruin problem on the positive quadrant," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 227-234, February.
- Mark B. Wise & Vineer Bhansali, 2008. "Correlated Random Walks and the Joint Survival Probability," Papers 0812.2000, arXiv.org.
- Marcos Escobar & Julio Hernandez, 2014. "A Note on the Distribution of Multivariate Brownian Extrema," International Journal of Stochastic Analysis, Hindawi, vol. 2014, pages 1-6, November.
- Xin Zhang, 2008. "On the Ruin Problem in a Markov-Modulated Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 10(2), pages 225-238, June.
- Gong, Lan & Badescu, Andrei L. & Cheung, Eric C.K., 2012. "Recursive methods for a multi-dimensional risk process with common shocks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 109-120.
- Pang, Guodong & Zheng, Yi, 2017. "On the functional and local limit theorems for Markov modulated compound Poisson processes," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 131-140.
- Cho-Jieh Chen & Harry Panjer, 2009. "A bridge from ruin theory to credit risk," Review of Quantitative Finance and Accounting, Springer, vol. 32(4), pages 373-403, May.
- Dickson, David C.M. & Qazvini, Marjan, 2018. "Ruin problems in Markov-modulated risk models," Annals of Actuarial Science, Cambridge University Press, vol. 12(1), pages 23-48, March.
- Stéphane Loisel, 2007. "Time to ruin, insolvency penalties and dividends in a Markov-modulated multi-risk model with common shocks," Post-Print hal-00165776, HAL.
- Yi Lu & Cary Tsai, 2007. "The Expected Discounted Penalty at Ruin for a Markov-Modulated Risk Process Perturbed by Diffusion," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(2), pages 136-149.
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- Albrecher, Hansjörg & Cheung, Eric C.K. & Liu, Haibo & Woo, Jae-Kyung, 2022. "A bivariate Laguerre expansions approach for joint ruin probabilities in a two-dimensional insurance risk process," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 96-118.
- Jingchao Li & Bihao Su & Zhenghong Wei & Ciyu Nie, 2022. "A Multinomial Approximation Approach for the Finite Time Survival Probability Under the Markov-modulated Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2169-2194, September.
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Keywords
Ruin probability; Insurance risk; Markov processes; Approximations; Multi-dimensional risk process;All these keywords.
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