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Asymptotics and Approximations of Ruin Probabilities for Multivariate Risk Processes in a Markovian Environment

Author

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  • G. A. Delsing

    (University of Amsterdam
    Rabobank)

  • M. R. H. Mandjes

    (University of Amsterdam
    CWI)

  • P. J. C. Spreij

    (University of Amsterdam
    Radboud University)

  • E. M. M. Winands

    (University of Amsterdam
    Rabobank)

Abstract

This paper develops asymptotics and approximations for ruin probabilities in a multivariate risk setting. We consider a model in which the individual reserve processes are driven by a common Markovian environmental process. We subsequently consider a regime in which the claim arrival intensity and transition rates of the environmental process are jointly sped up, and one in which there is (with overwhelming probability) maximally one transition of the environmental process in the time interval considered. The approximations are extensively tested in a series of numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09742-4
    DOI: 10.1007/s11009-019-09742-4
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    References listed on IDEAS

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    Cited by:

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    2. 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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