The study of basic risk processes by discrete-time non-homogeneous Markov processes
Authors:
G. D’Amico, F. Gismondi, J. Janssen, R. Manca, F. Petroni and E. Volpe di Prignano
Journal:
Theor. Probability and Math. Statist. 96 (2018), 27-43
MSC (2010):
Primary 60J10; Secondary 62P05
DOI:
https://doi.org/10.1090/tpms/1032
Published electronically:
October 5, 2018
MathSciNet review:
3666870
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Additional Information
Abstract: This paper elaborates how it is possible to calculate precisely the aggregate claim amount and the claim number by means of Markov reward models in a non-homogeneous time setting. More precisely, evolution equations of the non-homogeneous Markov reward processes are presented in a discounted environment for the calculation of the aggregate claim amount and in a non-discounted case for the calculation of the claim number. The underlying Markov process has a denumerable number of states. In the last section, an application of the proposed models is presented using real data obtained by merging databases of two small insurance companies. The results highlight the importance of the insured’s age in the calculation of the actuarial quantities.
References
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Additional Information
G. D’Amico
Affiliation:
Department of Pharmacy, University “G. d’Annunzio” of Chieti-Pescara, 66013 Chieti, Italy
F. Gismondi
Affiliation:
DSEA, University “Guglielmo Marconi”, 00193, Rome, Italy
J. Janssen
Affiliation:
Université Libre de Bruxelles, 1050 Bruxelles, Belgium
R. Manca
Affiliation:
MEMOTEF Department, University “La Sapienza” of Rome, 00185 Rome RM, Italy
Email:
raimondo.manca@uniroma1.it
F. Petroni
Affiliation:
Department of Business, University of Cagliari, 09124 Cagliari CA, Italy
E. Volpe di Prignano
Affiliation:
MEMOTEF Department, University “La Sapienza” of Rome, 00185 Rome RM, Italy
Keywords:
Aggregate claim amount process,
claim number process,
Markov chains,
reward processes,
non-homogeneity
Received by editor(s):
February 22, 2017
Published electronically:
October 5, 2018
Article copyright:
© Copyright 2018
American Mathematical Society