Fourier-cosine method for Gerber-Shiu functions. (English) Zbl 1314.91235

Summary: 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 F. Fang and C. W. Oosterlee [SIAM J. Sci. Comput. 31, No. 2, 826–848 (2008; Zbl 1186.91214)]. Our approximant of Gerber-Shiu functions under Lévy subordinator model has \(O(n)\) computational complexity in comparison with that of \(O(n \log n)\) 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 [the authors, J. Comput. Appl. Math. 281, 94–106 (2015; Zbl 1305.91163)], 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.


91G60 Numerical methods (including Monte Carlo methods)
91B30 Risk theory, insurance (MSC2010)
65T40 Numerical methods for trigonometric approximation and interpolation
42A10 Trigonometric approximation
60E10 Characteristic functions; other transforms
Full Text: DOI


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