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Some Explicit Solutions for the Joint Density of the Time of Ruin and the Deficit at Ruin

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  • Dickson, David C.M.

Abstract

Using probabilistic arguments we obtain an integral expression for the joint density of the time of ruin and the deficit at ruin. For the classical risk model, we obtain the bivariate Laplace transform of this joint density and invert it in the cases of individual claims distributed as Erlang(2) and as a mixture of two exponential distributions. As a consequence, we obtain explicit solutions for the density of the time of ruin.

Suggested Citation

  • Dickson, David C.M., 2008. "Some Explicit Solutions for the Joint Density of the Time of Ruin and the Deficit at Ruin," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 259-276, May.
    • Handle: RePEc:cup:astinb:v:38:y:2008:i:01:p:259-276_01
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    Cited by:

    1. Dickson, David C.M., 2016. "A note on some joint distribution functions involving the time of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 120-124.
    2. Gildas Ratovomirija, 2015. "Multivariate Stop loss Mixed Erlang Reinsurance risk: Aggregation, Capital allocation and Default risk," Papers 1501.07297, arXiv.org.
    3. Dickson, David C.M. & Li, Shuanming, 2010. "Finite time ruin problems for the Erlang(2) risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 12-18, February.

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