Leonenko, Mykola ![]() ![]() Item availability restricted. |
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Abstract
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 Cram´er–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.
Item Type: | Article |
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Status: | In Press |
Schools: | Schools > Mathematics |
Publisher: | Springer |
ISSN: | 1133-0686 |
Date of First Compliant Deposit: | 8 October 2025 |
Date of Acceptance: | 3 October 2025 |
Last Modified: | 09 Oct 2025 08:04 |
URI: | https://orca.cardiff.ac.uk/id/eprint/181473 |
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