An application of fractional differential equations to risk theory

Corina D. Constantinescu (), Jorge M. Ramirez and Wei R. Zhu
Additional contact information
Corina D. Constantinescu: University of Liverpool
Jorge M. Ramirez: Universidad Nacional de Colombia
Wei R. Zhu: University of Liverpool

Finance and Stochastics, 2019, vol. 23, issue 4, No 7, 1024 pages

Abstract: Abstract This paper defines a new class of fractional differential operators alongside a family of random variables whose density functions solve fractional differential equations equipped with these operators. These equations can be further used to construct fractional integro-differential equations for the ruin probabilities in collective renewal risk models, with inter-arrival time distributions from the aforementioned family. Gamma-time risk models and fractional Poisson risk models are two specific cases among them, whose ruin probabilities have explicit solutions when claim size distributions exhibit rational Laplace transforms.

Keywords: Ruin probability; Fractional differential operator; Collective risk model; 62P05; 60K05; 26A33 (search for similar items in EconPapers)
JEL-codes: C02 G22 G33 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://link.springer.com/10.1007/s00780-019-00400-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:finsto:v:23:y:2019:i:4:d:10.1007_s00780-019-00400-8

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

DOI: 10.1007/s00780-019-00400-8

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().