An application of fractional differential equations to risk theory

Constantinescu-Loeffen, DC ORCID: 0000-0002-5219-3022, Ramirez, Jorge M and Zhu, Wei (2019) An application of fractional differential equations to risk theory. Finance and Stochastics, 23. pp. 1001-1024.

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Official URL: https://link.springer.com/article/10.1007/s00780-0...

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.

Item Type:	Article
Uncontrolled Keywords:	ruin probability, fractional differential operator, collective risk model
Depositing User:	Symplectic Admin
Date Deposited:	12 Jul 2019 14:54
Last Modified:	19 Jan 2023 00:37
DOI:	10.1007/s00780-019-00400-8
Open Access URL:	https://link.springer.com/article/10.1007/s00780-0...
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3049665