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A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model

Author

Listed:
  • Jiechang Ruan

    (Department of Humanities and Social Sciences, Yibin Vocational & Technical College, Yibin 644003, China)

  • Wenguang Yu

    (School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China)

  • Ke Song

    (School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China)

  • Yihan Sun

    (School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China)

  • Yujuan Huang

    (School of Science, Shandong Jiaotong University, Jinan 250357, China)

  • Xinliang Yu

    (School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China)

Abstract

In this paper, we propose a new generalized Gerber–Shiu discounted penalty function for a compound Poisson risk model, which can be used to study the moments of the ruin time. First, by taking derivatives with respect to the original Gerber–Shiu discounted penalty function, we construct a relation between the original Gerber–Shiu discounted penalty function and our new generalized Gerber–Shiu discounted penalty function. Next, we use Laplace transform to derive a defective renewal equation for the generalized Gerber–Shiu discounted penalty function, and give a recursive method for solving the equation. Finally, when the claim amounts obey the exponential distribution, we give some explicit expressions for the generalized Gerber–Shiu discounted penalty function. Numerical illustrations are also given to study the effect of the parameters on the generalized Gerber–Shiu discounted penalty function.

Suggested Citation

  • Jiechang Ruan & Wenguang Yu & Ke Song & Yihan Sun & Yujuan Huang & Xinliang Yu, 2019. "A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model," Mathematics, MDPI, vol. 7(10), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:891-:d:270152
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    References listed on IDEAS

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