Probability of ruin within finite time and Cramér–Lundberg inequality for fractional risk processes
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Nikolai Leonenko [1]
;
Andrey Pepelyshev
[1]
;
Alois Pichler
[2]
;
Enrica Pirozzi
[3]
;
Xiangyun Meng
[1]
-
[1] Cardiff University
Cardiff University
Castle, Reino Unido
-
[2] Chemnitz University of Technology
Chemnitz University of Technology
Kreisfreie Stadt Chemnitz, Alemania
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[3] Universita della Campania Luigi Vanvitelli
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 35, Nº. 1, 2026, págs. 23-48
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
While the interarrival times of the classical Poisson process are exponentially distributed, complex systems often exhibit non-exponential patterns, motivating the use of the fractional Poisson process, in which interarrival times follow a Mittag–Leffler distribution. This paper investigates the associated risk process, describes its Cramér–Lundberg formula and establishes a relationship between the continuous premium rate and the fractional claim frequency. For a compound fractional risk process with exponential claims, we derive closed-form expressions for the finite-time ruin probability. Furthermore, for a general claim distribution, we provide ruin probability estimates that can serve as a basis for developing reinsurance strategies.
