Probability of ruin within finite time and Cramér-Lundberg inequality for fractional risk processes

Leonenko, Mykola ORCID: https://orcid.org/0000-0003-1932-4091, Pepelyshev, Andrey ORCID: https://orcid.org/0000-0001-5634-5559, Pichler, Alois, Pirozzi, Enrica and Meng, Xiangyun 2025. Probability of ruin within finite time and Cramér-Lundberg inequality for fractional risk processes. TEST 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
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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