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A Fourier-cosine method for finite-time ruin probabilities

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  • Lee, Wing Yan
  • Li, Xiaolong
  • Liu, Fangda
  • Shi, Yifan
  • Yam, Sheung Chi Phillip

Abstract

In this paper, we study the finite-time ruin probability in the risk model driven by a Lévy subordinator, by incorporating the popular Fourier-cosine method. Our interest is to propose a general approximation for any specified precision provided that the characteristic function of the Lévy Process is known. To achieve this, we derive an explicit integral expression for the finite-time ruin probability, which is expressed in terms of the density function and the survival function of Lt. Moreover, we apply the rearrangement inequality to further improve our approximations. In addition, with only mild and practically relevant assumptions, we prove that the approximation error can be made arbitrarily small (actually an algebraic convergence rate up to 3, which is the fastest possible approximant known upon all in the literature), and has a linear computation complexity in a number of terms of the Fourier-cosine expansion. The effectiveness of our results is demonstrated in various numerical studies; through these examples, the supreme power of the Fourier-cosine method is once demonstrated.

Suggested Citation

  • Lee, Wing Yan & Li, Xiaolong & Liu, Fangda & Shi, Yifan & Yam, Sheung Chi Phillip, 2021. "A Fourier-cosine method for finite-time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 256-267.
    • Handle: RePEc:eee:insuma:v:99:y:2021:i:c:p:256-267
    DOI: 10.1016/j.insmatheco.2021.03.001
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    4. Chongkai Xie & Honglong You, 2024. "A Threshold Estimator for Ruin Probability Using the Fourier-Cosine Method in the Wiener–Poisson Risk Model," Mathematics, MDPI, vol. 12(18), pages 1-14, September.

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