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Ruin problems in Markov-modulated risk models

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  • Dickson, David C.M.
  • Qazvini, Marjan

Abstract

Chen et al. (2014), studied a discrete semi-Markov risk model that covers existing risk models such as the compound binomial model and the compound Markov binomial model. We consider their model and build numerical algorithms that provide approximations to the probability of ultimate ruin and the probability and severity of ruin in a continuous time two-state Markov-modulated risk model. We then study the finite time ruin probability for a discrete m-state model and show how we can approximate the density of the time of ruin in a continuous time Markov-modulated model with more than two states.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:anacsi:v:12:y:2018:i:01:p:23-48_00
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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. 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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