Fractional risk process in insurance

Kumar, Arun, Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Pichler, Alois 2020. Fractional risk process in insurance. Mathematics and Financial Economics 14 , pp. 43-65. 10.1007/s11579-019-00244-y

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Abstract

The Poisson process suitably models the time of successive events and thus has numerous applications in statistics, in economics, it is also fundamental in queueing theory. Economic applications include trading and nowadays particularly high frequency trading. Of outstanding importance are applications in insurance, where arrival times of successive claims are of vital importance. It turns out, however, that real data do not always support the genuine Poisson process. This has lead to variants and augmentations such as time dependent and varying intensities, for example. This paper investigates the fractional Poisson process. We introduce the process and elaborate its main characteristics. The exemplary application considered here is the Carmér–Lundberg theory and the Sparre Andersen model. The fractional regime leads to initial economic stress. On the other hand we demonstrate that the average capital required to recover a company after ruin does not change when switching to the fractional Poisson regime. We finally address particular risk measures, which allow simple evaluations in an environment governed by the fractional Poisson process.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer Verlag
ISSN:	1862-9679
Date of First Compliant Deposit:	4 June 2019
Date of Acceptance:	6 June 2019
Last Modified:	06 Nov 2023 23:19
URI:	https://orca.cardiff.ac.uk/id/eprint/123153

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