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Ruin Probabilities for Two Classes of Risk Processes

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  • Li, Shuanming
  • Garrido, José

Abstract

We consider a risk model with two independent classes of insurance risks. We assume that the two independent claim counting processes are, respectively, Poisson and Sparre Andersen processes with generalized Erlang(2) claim inter-arrival times. The Laplace transform of the non-ruin probability is derived from a system of integro-differential equations. Explicit results can be obtained when the initial reserve is zero and the claim severity distributions of both classes belong to the Kn family of distributions. A relation between the ruin probability and the distribution of the supremum before ruin is identified. Finally, the Laplace transform of the non-ruin probability of a perturbed Sparre Andersen risk model with generalized Erlang(2) claim inter-arrival times is derived when the compound Poisson process converges weakly to a Wiener process.

Suggested Citation

  • Li, Shuanming & Garrido, José, 2005. "Ruin Probabilities for Two Classes of Risk Processes," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 61-77, May.
    • Handle: RePEc:cup:astinb:v:35:y:2005:i:01:p:61-77_01
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    Cited by:

    1. Covrig Mihaela & Serban Radu, 2008. "About Risk Process Estimation Techniques Employed By A Virtual Organization Which Is Directed Towards The Insurance Business," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 2(1), pages 841-847, May.
    2. He Liu & Zhenhua Bao, 2015. "On a Discrete Interaction Risk Model with Delayed Claims," JRFM, MDPI, vol. 8(4), pages 1-14, September.
    3. Diko, Peter & Usábel, Miguel, 2011. "A numerical method for the expected penalty-reward function in a Markov-modulated jump-diffusion process," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 126-131, July.
    4. Chadjiconstantinidis, Stathis & Papaioannou, Apostolos D., 2009. "Analysis of the Gerber-Shiu function and dividend barrier problems for a risk process with two classes of claims," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 470-484, December.

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