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On a Sparre Andersen Risk Model with Time-Dependent Claim Sizes and Jump-Diffusion Perturbation

Author

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  • Zhimin Zhang

    (Chongqing University)

  • Hailiang Yang

    (The University of Hong Kong)

  • Hu Yang

    (Chongqing University)

Abstract

In this paper, we consider a Sparre Andersen risk model where the interclaim time and claim size follow some bivariate distribution. Assuming that the risk model is also perturbed by a jump-diffusion process, we study the Gerber–Shiu functions when ruin is due to a claim or the jump-diffusion process. By using a q-potential measure, we obtain some integral equations for the Gerber–Shiu functions, from which we derive the Laplace transforms and defective renewal equations. When the joint density of the interclaim time and claim size is a finite mixture of bivariate exponentials, we obtain the explicit expressions for the Gerber–Shiu functions.

Suggested Citation

  • Zhimin Zhang & Hailiang Yang & Hu Yang, 2012. "On a Sparre Andersen Risk Model with Time-Dependent Claim Sizes and Jump-Diffusion Perturbation," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 973-995, December.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:4:d:10.1007_s11009-011-9215-1
    DOI: 10.1007/s11009-011-9215-1
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    References listed on IDEAS

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    14. Cheung, Eric C.K. & Landriault, David & Willmot, Gordon E. & Woo, Jae-Kyung, 2010. "Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 117-126, February.
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    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. Zhou, Zhongbao & Xiao, Helu & Deng, Yingchun, 2015. "Markov-dependent risk model with multi-layer dividend strategy," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 273-286.

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