The time to ruin and the number of claims until ruin for phase-type claims
We consider a renewal risk model with phase-type claims, and obtain an explicit expression for the joint transform of the time to ruin and the number of claims until ruin, with a penalty function applied to the deficit at ruin. The approach is via the duality between a risk model with phase-type claims and a particular single server queueing model with phase-type customer interarrival times; see Frostig (2004). This result specializes to one for the probability generating function of the number of claims until ruin. We obtain explicit expressions for the distribution of the number of claims until ruin for exponentially distributed claims when the inter-claim times have an Erlang-n distribution.
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Volume (Year): 51 (2012)
Issue (Month): 1 ()
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- Borovkov, Konstantin A. & Dickson, David C.M., 2008. "On the ruin time distribution for a Sparre Andersen process with exponential claim sizes," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1104-1108, June.
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- Landriault, David & Willmot, Gordon, 2008. "On the Gerber-Shiu discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 600-608, April.
- Ahn, Soohan & Badescu, Andrei L., 2007. "On the analysis of the Gerber-Shiu discounted penalty function for risk processes with Markovian arrivals," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 234-249, September.
- Panjer, H. H. & Willmot, G. E., 1982. "Recursions for Compound Distributions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 13(01), pages 1-12, June.
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