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Computing the Gerber–Shiu function by frame duality projection

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  • Wenyuan Wang
  • Zhimin Zhang

Abstract

Inspired by some works of Kirkby, J. L. [2015. Efficient option pricing by frame duality with the fast Fourier transform. SIAM Journal on Financial Mathematics 6(1), 713–747; 2016. An efficient transform method for Asian option pricing. SIAM Journal on Financial Mathematics 7(1), 845–892], we present a systematic study on effectively computing the Gerber–Shiu function in the Lévy risk model, where the frame duality projection is used for approximation. By introducing an auxiliary function, we provide a smooth extension of the Gerber–Shiu function, which has closed-form Fourier transform and is differentiable over the whole real line under some conditions. The objective function is approximated by its frame duality projection onto a Riesz basis, and the projection coefficients are readily computed by the fast Fourier transform algorithm. Error analysis is made and the effectiveness of our results will be further illustrated in the numerical experiments.

Suggested Citation

  • Wenyuan Wang & Zhimin Zhang, 2019. "Computing the Gerber–Shiu function by frame duality projection," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(4), pages 291-307, April.
    • Handle: RePEc:taf:sactxx:v:2019:y:2019:i:4:p:291-307
    DOI: 10.1080/03461238.2018.1557739
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    Cited by:

    1. Zan Yu & Lianzeng Zhang, 2024. "Computing the Gerber-Shiu function with interest and a constant dividend barrier by physics-informed neural networks," Papers 2401.04378, arXiv.org.

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