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The Gerber-shiu Expected Discounted Penalty-reward Function under an Affine Jump-diffusion Model

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  • Avram, Florin
  • Usabel, Miguel

Abstract

We provide a unified analytical treatment of first passage problems under an affine state-dependent jump-diffusion model (with drift and volatility depending linearly on the state). Our proposed model, that generalizes several previously studied cases, may be used for example for obtaining probabilities of ruin in the presence of interest rates under the rational investement strategies proposed by Berk & Green (2004).

Suggested Citation

  • Avram, Florin & Usabel, Miguel, 2004. "The Gerber-shiu Expected Discounted Penalty-reward Function under an Affine Jump-diffusion Model," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 461-481, November.
    • Handle: RePEc:cup:astinb:v:38:y:2008:i:02:p:461-481_01
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    Cited by:

    1. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
    2. Yue He & Reiichiro Kawai & Yasutaka Shimizu & Kazutoshi Yamazaki, 2022. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Papers 2203.10680, arXiv.org, revised Dec 2022.
    3. Florin Avram & Jose-Luis Perez-Garmendia, 2019. "A Review of First-Passage Theory for the Segerdahl-Tichy Risk Process and Open Problems," Risks, MDPI, vol. 7(4), pages 1-21, November.

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