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Probabilités de Ruine pour une Classe de Modèles de Risque Semi-Markoviens

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  • Janssen, Jacques
  • Reinhard, Jean-Marie

Abstract

We consider particular semi-Markov risk models M/SM and /SM for which the interarrival distributions are exponential with parameters depending of the risk type. We obtain theoretical expressions for the ruin probabilities on an infinite horizon. In the special case of exponential distributions for the claim amounts, ruin probabilities are in both models solutions of linear differential systems. These systems are explicitly solved when there are only two risk types.

Suggested Citation

  • Janssen, Jacques & Reinhard, Jean-Marie, 1985. "Probabilités de Ruine pour une Classe de Modèles de Risque Semi-Markoviens," ASTIN Bulletin, Cambridge University Press, vol. 15(2), pages 123-133, November.
    • Handle: RePEc:cup:astinb:v:15:y:1985:i:02:p:123-133_00
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    Cited by:

    1. Guglielmo D’Amico & Fulvio Gismondi & Jacques Janssen & Raimondo Manca, 2015. "Discrete Time Homogeneous Markov Processes for the Study of the Basic Risk Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 983-998, December.
    2. Schmidli, Hanspeter, 2001. "Distribution of the first ladder height of a stationary risk process perturbed by [alpha]-stable Lévy motion," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 13-20, February.
    3. O. J. Boxma & M. R. H. Mandjes, 2022. "Queueing and risk models with dependencies," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 69-86, October.
    4. Zhou, Zhongbao & Xiao, Helu & Deng, Yingchun, 2015. "Markov-dependent risk model with multi-layer dividend strategy," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 273-286.
    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. Siegl, Thomas & Tichy, Robert F., 1999. "A process with stochastic claim frequency and a linear dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 51-65, March.
    7. Giuseppe Di Biase & Jacques Janssen & Raimondo Manca, 2010. "A Non-Homogeneous Continuous Time Semi-Markov Model for the Study of Accumulated Claim Process," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 227-235, June.
    8. 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.
    9. Cossette, Helene & Landriault, David & Marceau, Etienne, 2004. "Compound binomial risk model in a markovian environment," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 425-443, October.

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