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Fractional Poisson Process: Long-Range Dependence and Applications in Ruin Theory

Part of: Other special functions Special processes Mathematical economics Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Romain Biard  and
Bruno Saussereau
Romain Biard*
Affiliation:
Laboratoire de Mathématiques de Besançon
Bruno Saussereau*
Affiliation:
Laboratoire de Mathématiques de Besançon
*
∗ Postal address: Laboratoire de mathématiques de Besançon, UMR CNRS 6623, 16 route de Gray, 25030 Besançon, France.
∗ Postal address: Laboratoire de mathématiques de Besançon, UMR CNRS 6623, 16 route de Gray, 25030 Besançon, France.
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Abstract

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We study a renewal risk model in which the surplus process of the insurance company is modelled by a compound fractional Poisson process. We establish the long-range dependence property of this nonstationary process. Some results for ruin probabilities are presented under various assumptions on the distribution of the claim sizes.

Keywords

Fractional Poisson processrenewal processlong-range dependenceruin probability

MSC classification

Primary: 60G22: Fractional processes, including fractional Brownian motion 60G55: Point processes 91B30: Risk theory, insurance
Secondary: 60K05: Renewal theory 33E12: Mittag-Leffler functions and generalizations
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 3 , September 2014 , pp. 727 - 740
Copyright
© Applied Probability Trust 

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