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On a multi-dimensional risk model with regime switching

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  • Wang, Guanqing
  • Wang, Guojing
  • Yang, Hailiang

Abstract

We consider an insurer with n(n≥2) classes of insurance business. The surplus process for each class of insurance business is assumed to follow a compound Cox risk process. Assume that n surplus processes are correlated with thinning dependence and regime switching. By summing up the n surplus processes we obtain a correlated risk process. Upper bounds for the ruin probability under certain assumptions are derived. The joint ruin probability for n classes of insurance business, the distribution of the number of the ruined business classes in a finite time interval and the Laplace transform of the ruin time of the correlated risk process are investigated. Some closed form results are obtained. Numerical examples are presented to explain how the collection of insurance risk increases the solvency of an insurer.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:68:y:2016:i:c:p:73-83
    DOI: 10.1016/j.insmatheco.2016.03.003
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    References listed on IDEAS

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    Cited by:

    1. Teng, Ye & Zhang, Zhimin, 2023. "Finite-time expected present value of operating costs until ruin in a Cox risk model with periodic observation," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    2. Gajek, Lesław & Rudź, Marcin, 2018. "Banach Contraction Principle and ruin probabilities in regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 45-53.
    3. Chao Xu & Yinghui Dong & Guojing Wang, 2019. "The pricing of defaultable bonds under a regime-switching jump-diffusion model with stochastic default barrier," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(9), pages 2185-2205, May.
    4. Gajek, Lesław & Rudź, Marcin, 2017. "A generalization of Gerber’s inequality for ruin probabilities in risk-switching models," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 236-240.

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