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.
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 |
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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: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3049665 |