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On the joint distribution of surplus before and after ruin under a Markovian regime switching model

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  • Ng, Andrew C.Y.
  • Yang, Hailiang

Abstract

We consider a Markovian regime switching insurance risk model (also called Markov-modulated risk model). The closed form solutions for the joint distribution of surplus before and after ruin when the initial surplus is zero or when the claim size distributions are phase-type distributed are obtained.

Suggested Citation

  • Ng, Andrew C.Y. & Yang, Hailiang, 2006. "On the joint distribution of surplus before and after ruin under a Markovian regime switching model," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 244-266, February.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:2:p:244-266
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    References listed on IDEAS

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    1. Dickson, David C. M., 1992. "On the distribution of the surplus prior to ruin," Insurance: Mathematics and Economics, Elsevier, vol. 11(3), pages 191-207, October.
    2. Mary Hardy, 2001. "A Regime-Switching Model of Long-Term Stock Returns," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 41-53.
    3. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    4. Li, Shuanming & Garrido, Jose, 2004. "On ruin for the Erlang(n) risk process," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 391-408, June.
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    Cited by:

    1. Lu, Yi & Li, Shuanming, 2009. "The Markovian regime-switching risk model with a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 296-303, April.
    2. Boudreault, Mathieu & Cossette, Hélène & Marceau, Étienne, 2014. "Risk models with dependence between claim occurrences and severities for Atlantic hurricanes," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 123-132.
    3. F. Baltazar-Larios & Luz Judith R. Esparza, 2022. "Statistical Inference for Partially Observed Markov-Modulated Diffusion Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 571-593, June.
    4. Ramírez-Cobo, Pepa & Carrizosa, Emilio & Lillo, Rosa E., 2021. "Analysis of an aggregate loss model in a Markov renewal regime," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    5. Chen, Mi & Yuen, Kam Chuen & Guo, Junyi, 2014. "Survival probabilities in a discrete semi-Markov risk model," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 205-215.
    6. Zhu, Jinxia & Yang, Hailiang, 2008. "Ruin theory for a Markov regime-switching model under a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 311-318, February.
    7. 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.
    8. Ivanovs, Jevgenijs, 2013. "A note on killing with applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 29-34.
    9. Chen, Xu & Xiao, Ting & Yang, Xiang-qun, 2014. "A Markov-modulated jump-diffusion risk model with randomized observation periods and threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 76-83.
    10. Wang, Guanqing & Wang, Guojing & Yang, Hailiang, 2016. "On a multi-dimensional risk model with regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 73-83.
    11. Ehyter Matías Martín-González & Antonio Murillo-Salas & Henry Pantí, 2022. "Gerber-Shiu Function for a Class of Markov-Modulated Lévy Risk Processes with Two-Sided Jumps," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2779-2800, December.
    12. Hyunjoo Yoo & Bara Kim & Jeongsim Kim & Jiwook Jang, 2020. "Transform approach for discounted aggregate claims in a risk model with descendant claims," Annals of Operations Research, Springer, vol. 293(1), pages 175-192, October.
    13. Li, Jingchao & Dickson, David C.M. & Li, Shuanming, 2015. "Some ruin problems for the MAP risk model," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 1-8.
    14. 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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