Finite-time ruin probabilities using bivariate Laguerre series

Eric C. K. Cheung, Hayden Lau, Gordon E. Willmot and Jae-Kyung Woo

Scandinavian Actuarial Journal, 2023, vol. 2023, issue 2, 153-190

Abstract: In this paper, we revisit the finite-time ruin probability in the classical compound Poisson risk model. Traditional general solutions to finite-time ruin problems are usually expressed in terms of infinite sums involving the convolutions related to the claim size distribution and their integrals, which can typically be evaluated only in special cases where the claims follow exponential or (more generally) mixed Erlang distribution. We propose to tackle the partial integro-differential equation satisfied by the finite-time ruin probability and develop a new approach to obtain a solution in terms of bivariate Laguerre series as a function of the initial surplus level and the time horizon for a large class of light-tailed claim distributions. To illustrate the versatility and accuracy of our proposed method which is easy to implement, numerical examples are provided for claim amount distributions such as generalized inverse Gaussian, Weibull and truncated normal where closed-form convolutions are not available in the literature.

Date: 2023
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1080/03461238.2022.2089051 (text/html)
Access to full text is restricted to subscribers.

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:taf:sactxx:v:2023:y:2023:i:2:p:153-190

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/sact20

DOI: 10.1080/03461238.2022.2089051

Access Statistics for this article

Scandinavian Actuarial Journal is currently edited by Boualem Djehiche

More articles in Scandinavian Actuarial Journal from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().