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The ruin time under the Sparre-Andersen dual model

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  • Yang, Chen
  • Sendova, Kristina P.

Abstract

In this paper, we study the Sparre-Andersen dual risk model in which the times between positive gains are independently and identically distributed and have a generalized Erlang-n distribution. An important difference between this model and some other models such as the Erlang-n dual risk model is that the roots to the generalized Lundberg’s equation are not necessarily distinct. Hence, we derive an explicit expression for the Laplace transform of the ruin time, which involves multiple roots. Also, we apply our approach for obtaining the expected discounted dividends when the threshold-dividend strategy discussed by Ng (2009) is implemented under the Sparre-Andersen model with Erlang-n distribution of the inter-event times. In particular, we derive an explicit form of the expected discounted dividends when jump sizes are exponential.

Suggested Citation

  • Yang, Chen & Sendova, Kristina P., 2014. "The ruin time under the Sparre-Andersen dual model," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 28-40.
    • Handle: RePEc:eee:insuma:v:54:y:2014:i:c:p:28-40
    DOI: 10.1016/j.insmatheco.2013.10.012
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    References listed on IDEAS

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    1. Ng, Andrew C.Y., 2009. "On a dual model with a dividend threshold," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 315-324, April.
    2. Avanzi, Benjamin & U. Gerber, Hans & S.W. Shiu, Elias, 2007. "Optimal dividends in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 111-123, July.
    3. Albrecher, Hansjörg & Badescu, Andrei & Landriault, David, 2008. "On the dual risk model with tax payments," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1086-1094, June.
    4. Lanpeng Ji & Chunsheng Zhang, 2012. "Analysis of the multiple roots of the Lundberg fundamental equation in the PH (n) risk model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(1), pages 73-90, January.
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    Cited by:

    1. Goffard, Pierre-Olivier & Lefèvre, Claude, 2018. "Duality in ruin problems for ordered risk models," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 44-52.
    2. Pierre-Olivier Goffard & Claude Lefèvre, 2018. "Duality in ruin problems for ordered risk models," Post-Print hal-01398910, HAL.
    3. Arash Fahim & Lingjiong Zhu, 2016. "Asymptotic Analysis for Optimal Dividends in a Dual Risk Model," Papers 1601.03435, arXiv.org, revised Dec 2022.
    4. Lingjiong Zhu, 2023. "A delayed dual risk model," Papers 2301.06450, arXiv.org.
    5. Arash Fahim & Lingjiong Zhu, 2015. "Optimal Investment in a Dual Risk Model," Papers 1510.04924, arXiv.org, revised Feb 2023.
    6. Lingjiong Zhu, 2015. "A State-Dependent Dual Risk Model," Papers 1510.03920, arXiv.org, revised Feb 2023.
    7. Dimitrova, Dimitrina S. & Kaishev, Vladimir K. & Zhao, Shouqi, 2015. "On finite-time ruin probabilities in a generalized dual risk model with dependence," European Journal of Operational Research, Elsevier, vol. 242(1), pages 134-148.

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