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On a Class of Renewal Risk Processes

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  • David Dickson

Abstract

In this paper I show how methods that have been applied to derive results for the classical risk process can be adapted to derive results for a class of risk processes in which claims occur as a renewal process. In particular, claims occur as an Erlang process. I consider the problem of finding the survival probability for such risk processes and then derive expressions for the probability and severity of ruin and for the probability of absorption by an upper barrier. Finally, I apply these results to consider the problem of finding the distribution of the maximum deficit during the period from ruin to recovery to surplus level 0.

Suggested Citation

  • David Dickson, 1998. "On a Class of Renewal Risk Processes," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(3), pages 60-68.
    • Handle: RePEc:taf:uaajxx:v:2:y:1998:i:3:p:60-68
    DOI: 10.1080/10920277.1998.10595723
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    Cited by:

    1. Tsai, Cary Chi-Liang & Sun, Li-juan, 2004. "On the discounted distribution functions for the Erlang(2) risk process," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 5-19, August.
    2. Yuen, Kam C. & Guo, Junyi & Wu, Xueyuan, 2002. "On a correlated aggregate claims model with Poisson and Erlang risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 205-214, October.
    3. 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.
    4. Sun, Lijuan & Yang, Hailiang, 2004. "On the joint distributions of surplus immediately before ruin and the deficit at ruin for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 121-125, February.
    5. Politis, Konstadinos, 2005. "Bounds for the probability and severity of ruin in the Sparre Andersen model," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 165-177, April.
    6. Psarrakos, Georgios, 2010. "On the DFR property of the compound geometric distribution with applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 428-433, December.
    7. Leveille, Ghislain & Garrido, Jose, 2001. "Moments of compound renewal sums with discounted claims," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 217-231, April.
    8. 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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