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Article: Fourier-cosine method for ruin probabilities

TitleFourier-cosine method for ruin probabilities
Authors
KeywordsFourier-cosine method
Gibbs phenomena
PollaczekKhinchin formula
Rearrangement inequalities
Ruin probabilities
Summation by parts
Issue Date2015
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cam
Citation
Journal of Computational and Applied Mathematics, 2015, v. 281, p. 94-106 How to Cite?
AbstractIn theory, ruin probabilities in classical insurance risk models can be expressed in terms of an infinite sum of convolutions, but its inherent complexity makes efficient computation almost impossible. In contrast, Fourier transforms of convolutions could be evaluated in a far simpler manner. This feature aligns with the heuristic of the recently popular work by Fang and Oosterlee, in particular, they developed a numerical method based on Fourier transform for option pricing. We here promote their philosophy to ruin theory. In this paper, we not only introduce the Fourier-cosine method to ruin theory, which has O(n)O(n) computational complexity, but we also enhance the error bound for our case that are not immediate from Fang and Oosterlee (2009). We also suggest a robust method on estimation of ruin probabilities with respect to perturbation of the moments of both claim size and claim arrival distributions. Rearrangement inequality will also be adopted to amplify the Fourier-cosine method, resulting in an effective global estimation.
Persistent Identifierhttp://hdl.handle.net/10722/214204
ISSN
2023 Impact Factor: 2.1
2023 SCImago Journal Rankings: 0.858
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChau, KW-
dc.contributor.authorYam, SCP-
dc.contributor.authorYang, H-
dc.date.accessioned2015-08-21T10:54:06Z-
dc.date.available2015-08-21T10:54:06Z-
dc.date.issued2015-
dc.identifier.citationJournal of Computational and Applied Mathematics, 2015, v. 281, p. 94-106-
dc.identifier.issn0377-0427-
dc.identifier.urihttp://hdl.handle.net/10722/214204-
dc.description.abstractIn theory, ruin probabilities in classical insurance risk models can be expressed in terms of an infinite sum of convolutions, but its inherent complexity makes efficient computation almost impossible. In contrast, Fourier transforms of convolutions could be evaluated in a far simpler manner. This feature aligns with the heuristic of the recently popular work by Fang and Oosterlee, in particular, they developed a numerical method based on Fourier transform for option pricing. We here promote their philosophy to ruin theory. In this paper, we not only introduce the Fourier-cosine method to ruin theory, which has O(n)O(n) computational complexity, but we also enhance the error bound for our case that are not immediate from Fang and Oosterlee (2009). We also suggest a robust method on estimation of ruin probabilities with respect to perturbation of the moments of both claim size and claim arrival distributions. Rearrangement inequality will also be adopted to amplify the Fourier-cosine method, resulting in an effective global estimation.-
dc.languageeng-
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cam-
dc.relation.ispartofJournal of Computational and Applied Mathematics-
dc.rights© 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjectFourier-cosine method-
dc.subjectGibbs phenomena-
dc.subjectPollaczekKhinchin formula-
dc.subjectRearrangement inequalities-
dc.subjectRuin probabilities-
dc.subjectSummation by parts-
dc.titleFourier-cosine method for ruin probabilities-
dc.typeArticle-
dc.identifier.emailChau, KW: kiwaic@HKUCC-COM.hku.hk-
dc.identifier.emailYang, H: hlyang@hku.hk-
dc.identifier.authorityYang, H=rp00826-
dc.description.naturepostprint-
dc.identifier.doi10.1016/j.cam.2014.12.014-
dc.identifier.scopuseid_2-s2.0-84920648207-
dc.identifier.hkuros248422-
dc.identifier.volume281-
dc.identifier.spage94-
dc.identifier.epage106-
dc.identifier.isiWOS:000350529500008-
dc.publisher.placeNetherlands-
dc.identifier.issnl0377-0427-

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