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Discrete Time Homogeneous Markov Processes for the Study of the Basic Risk Processes

Author

Listed:
  • Guglielmo D’Amico

    (Università G. d’Annunzio di Chieti)

  • Fulvio Gismondi

    (University Guglielmo Marconi)

  • Jacques Janssen

    (Honorary professor at the Solvay Business School Universitè Libre de Bruxelles)

  • Raimondo Manca

    (Università di Roma La Sapienza)

Abstract

In this paper Markov models useful for following the time evolution of the aggregate claim amount and the claim number in the homogeneous time environment are presented. More precisely the homogeneous Markov reward processes in both discounted and not discounted cases are applied to solve the aggregate claim amount and the claim number processes respectively. In the last section the application of the proposed models is presented. Two different real-world databases are mixed for the construction of input data.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:4:d:10.1007_s11009-014-9416-5
    DOI: 10.1007/s11009-014-9416-5
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    References listed on IDEAS

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    1. 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.
    2. V. S. Borkar & S. P. Meyn, 2002. "Risk-Sensitive Optimal Control for Markov Decision Processes with Monotone Cost," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 192-209, February.
    3. Janssen, Jacques, 1980. "Some Transient Results on the M/SM/1 Special Semi-Markov Model in Risk and Queueing Theories," ASTIN Bulletin, Cambridge University Press, vol. 11(1), pages 41-51, June.
    4. Ronald A. Howard & James E. Matheson, 1972. "Risk-Sensitive Markov Decision Processes," Management Science, INFORMS, vol. 18(7), pages 356-369, March.
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    Cited by:

    1. Guglielmo D’Amico & Filippo Petroni & Salvatore Vergine, 2021. "An Analysis of a Storage System for a Wind Farm with Ramp-Rate Limitation," Energies, MDPI, vol. 14(13), pages 1-25, July.
    2. Guglielmo D’Amico & Shakti Singh & Dharmaraja Selvamuthu, 2023. "Analysis of fair fee in guaranteed lifelong withdrawal and Markovian health benefits," Annals of Finance, Springer, vol. 19(3), pages 383-400, September.

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