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Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier

Author

Listed:
  • Maite Teresa Marmol Jimenez
  • M. Mercedes Claramunt Bielsa

    (Universitat de Barcelona)

Abstract

In this paper we analyze the time of ruin in a risk process with the interclaim times being Erlang(n) distributed and a constant dividend barrier. We obtain an integro-differential equation for the Laplace Transform of the time of ruin. Explicit solutions for the moments of the time of ruin are presented when the individual claim amounts have a distribution with rational Laplace transform. Finally, some numerical results and a compare son with the classical risk model, with interclaim times following an exponential distribution, are given.

Suggested Citation

  • Maite Teresa Marmol Jimenez & M. Mercedes Claramunt Bielsa, 2006. "Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier," Working Papers in Economics 157, Universitat de Barcelona. Espai de Recerca en Economia.
    • Handle: RePEc:bar:bedcje:2006157
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    References listed on IDEAS

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    1. Dickson, David C.M. & Waters, Howard R., 2002. "The Distribution of the time to Ruin in the Classical Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 299-313, November.
    2. Ren, Jiandong, 2005. "The expected value of the time of ruin and the moments of the discounted deficit at ruin in the perturbed classical risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 505-521, December.
    3. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    4. Albrecher, Hansjorg & Claramunt, M.Merce & Marmol, Maite, 2005. "On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 324-334, October.
    5. Dickson, David C. M. & Hipp, Christian, 2001. "On the time to ruin for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 333-344, December.
    6. Drekic, Steve & Willmot, Gordon E., 2003. "On the Density and Moments of the Time of Ruin with Exponential Claims," ASTIN Bulletin, Cambridge University Press, vol. 33(1), pages 11-21, May.
    7. Li, Shuanming & Garrido, Jose, 2004. "On a class of renewal risk models with a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 691-701, December.
    8. Lin, X. Sheldon & Willmot, Gordon E., 2000. "The moments of the time of ruin, the surplus before ruin, and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 19-44, August.
    9. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
    10. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
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    Cited by:

    1. Art Durnev & Sergei Guriev, 2007. "The Resource Curse: A Corporate Transparency Channel," Working Papers w0108, New Economic School (NES).

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    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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