 Fourier-cosine method for Gerber–Shiu functionsK.W. Chau, S.C.P. Yam and H. Yang Insurance: Mathematics and Economics, 2015, vol. 61, issue C, 170-180 Abstract: In this article, we provide a systematic study on effectively approximating the Gerber–Shiu functions, which is a hardly touched topic in the current literature, by incorporating the recently popular Fourier-cosine method. Fourier-cosine method has been a prevailing numerical method in option pricing theory since the work of Fang and Oosterlee (2009). Our approximant of Gerber–Shiu functions under Lévy subordinator model has O(n) computational complexity in comparison with that of O(nlogn) via the fast Fourier transform algorithm. Also, for Gerber–Shiu functions within our proposed refined Sobolev space, we introduce an explicit error bound, which seems to be absent from the literature. In contrast with our previous work (Chau et al., 2015), this error bound is more conservative without making heavy assumptions on the Fourier transform of the Gerber–Shiu function. The effectiveness of our result will be further demonstrated in the numerical studies. Keywords: Gerber–Shiu functions; Lévy subordinator; Fourier-cosine method; Sobolev embedding theorem; Harmonic analysis (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:61:y:2015:i:c:p:170-180 DOI: 10.1016/j.insmatheco.2015.01.008 Access Statistics for this article Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu More articles in Insurance: Mathematics and Economics from Elsevier |
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