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A Note on a Generalized Discounted Penalty Function in a Sparre Andersen Risk Model Perturbed by Diffusion

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Listed:
  • Chaolin Liu
  • Zhimin Zhang

Abstract

We consider a Sparre Andersen risk model perturbed by diffusion where the interclaim times are generalized Erlang(n) distribution. Generalized discounted penalty functions incorporating the maximum surplus before ruin are studied. We derive the integrodifferential equations and give the solutions for the generalized discounted penalty functions.

Suggested Citation

  • Chaolin Liu & Zhimin Zhang, 2013. "A Note on a Generalized Discounted Penalty Function in a Sparre Andersen Risk Model Perturbed by Diffusion," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:759352
    DOI: 10.1155/2013/759352
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    References listed on IDEAS

    as
    1. Shuanming Li, 2006. "The distribution of the dividend payments in the compound poisson risk model perturbed by diffusion," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2006(2), pages 73-85.
    2. Andreas E. Kyprianou, 2006. "Introductory Lectures on Fluctuations of Lévy Processes with Applications," Springer Books, Springer, number 978-3-540-31343-4, March.
    3. Cheung, Eric C.K. & Landriault, David, 2010. "A generalized penalty function with the maximum surplus prior to ruin in a MAP risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 127-134, February.
    4. Li, Shuanming & Lu, Yi, 2008. "The Decompositions of the Discounted Penalty Functions and Dividends-Penalty Identity in a Markov-Modulated Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 53-71, May.
    5. Li, Shuanming & Dickson, David C.M., 2006. "The maximum surplus before ruin in an Erlang(n) risk process and related problems," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 529-539, June.
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