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Methodology and Computing in Applied Probability

, Volume 17, Issue 4, pp 983–998 | Cite as

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

  • Guglielmo D’Amico
  • Fulvio Gismondi
  • Jacques Janssen
  • Raimondo MancaEmail author
Article

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.

Keywords

Aggregate claim amount process Claim number Markov chains Reward processes Homogeneity 

Mathematics Subject Classification (2010)

60J20 91G99 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Guglielmo D’Amico
    • 1
  • Fulvio Gismondi
    • 2
  • Jacques Janssen
    • 3
  • Raimondo Manca
    • 4
    Email author
  1. 1.Dipartimento di FarmaciaUniversità G. d’Annunzio di ChietiChietiItaly
  2. 2.University Guglielmo MarconiRomaItaly
  3. 3.Honorary professor at the Solvay Business School Universitè Libre de BruxellesBruxellesBelgium
  4. 4.Dipartimento di Metodi e modelli per l’Economia, il Territorio e la FinanzaUniversità di Roma La SapienzaRomaItaly

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