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On the Ruin Problem in a Markov-Modulated Risk Model

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  • Xin Zhang

    (Nankai University)

Abstract

In this paper, we consider the compound Poisson risk model influenced by an external Markovian environment process, i.e. Markov-modulated compound Poisson model. The explicit Laplace transforms of Gerber–Shiu functions are obtained, while the explicit Gerber–Shiu functions are derived for the K n -family claim size distributions in the two-states case.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:2:d:10.1007_s11009-007-9044-4
    DOI: 10.1007/s11009-007-9044-4
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    References listed on IDEAS

    as
    1. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    2. 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.
    3. Dickson, David C. M. & Hipp, Christian, 2001. "On the time to ruin for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 333-344, December.
    4. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
    5. Lu, Yi & Li, Shuanming, 2005. "On the probability of ruin in a Markov-modulated risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 522-532, December.
    6. Albrecher, Hansjorg & Boxma, Onno J., 2005. "On the discounted penalty function in a Markov-dependent risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 650-672, December.
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    Cited by:

    1. G. A. Delsing & M. R. H. Mandjes & P. J. C. Spreij & E. M. M. Winands, 2020. "Asymptotics and Approximations of Ruin Probabilities for Multivariate Risk Processes in a Markovian Environment," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 927-948, September.
    2. Simon Pojer & Stefan Thonhauser, 2023. "The Markovian Shot-noise Risk Model: A Numerical Method for Gerber-Shiu Functions," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    3. 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.
    4. 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.
    5. 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.
    6. 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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