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Blätter der DGVFM

, Volume 25, Issue 3, pp 521–533 | Cite as

On the distribution of the surplus prior to ruin and at ruin in a discrete semi-markov risk model

  • Mohammed Snoussi
Article
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Summary

In this paper we extend the work of Reinhard and Snoussi (2000, 2001a, 2001b) by developing a recursive system for finding the distribution of the surplus prior to ruin and at ruin in a discrete semi-Markov risk model.

Keywords

Risk Model Claim Amount Initial Surplus Ruin Probability Markovian Environment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Über die Verteilung des Überschusses vor und zum Zeitpunkt des Ruins in Semi-Markov-Risikomodellen

Zusammenfassung

In diesem Aufsatz wurde die Arbeit von Reinhard und Snoussi (2000, 2001a, 2001b) um die Entwicklung eines rekursiven Systems zum Finden der Verteilung des Überschusses vor und zum Zeitpunkt des Ruins in Semi-Markov-Risikomodellen erweitert.

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References

  1. [1]
    Asmussen, S. (1989): Risk theory in a markovian environment. Scand. Actuariat J., 66–100.Google Scholar
  2. [2]
    Dickson, D. C. M. (1992): On the distribution of the surplus prior to ruin. Insurance: Mathematics and Economics 11, 191–207.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Dickson, D. C. M., Egidio Dos Ries, A. D., andWaters, H. R. (1995): Some stable algorithms in ruin theory and their applications. Astin Bulletin 25, 153–175.CrossRefGoogle Scholar
  4. [4]
    Dufresne, F. (1989): Probabilité et sévérité de la ruine modèle classique de la théorie du risque collectif et une de ses extensions. Ph.D. thesis, Université de Lausanne.Google Scholar
  5. [5]
    Dufresne, F. andGerber, H. U. (1988): The surplus immediately before and at ruin, and the amount of the claim causing ruin. Insurance: Mathematics and Economics 7, 193–199.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Gerber, H. U. andShiu, E. S. W. (1997): The joint distribution of the time of ruin, the surplus immediately before ruin, and the dificit at ruin. Insurance: Mathematics and Economics 21, 129–137.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Gerber, H. U. andShiu, E. S. W. (1998): On the time value of ruin. North American Actuarial Journal 1998, 48–78.MathSciNetGoogle Scholar
  8. [8]
    Grandell, J. (1991): Aspects of Risk Theory. Springer Series in Statistics.Google Scholar
  9. [9]
    Janssen, J. (1970): Sur une généralisation du concept de promenade aléatoire sur la droite réelle. Ann. Ins. H. Poincaré, B, VI, 249–269.Google Scholar
  10. [10]
    Janssen, J. andReinhard, J. M. (1985): Probalitiés de ruine pour une classe de modèles de risque semi-Markoviens. Astin Bulletin 15, 123–133.CrossRefGoogle Scholar
  11. [11]
    Newbould, M. (1973): A classification of a random walk defined on a finite Markov chain. Z. Wahrscheinlichkeitstheorie. verw. Geb., 26, 95–104.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Panjer, H. H. andWang, S. (1993): On the stability of recursive formulas. Astin Bulletin 23, 227–258.CrossRefGoogle Scholar
  13. [13]
    Reinhard, J. M. (1984): On a class of semi-Markov risk models obtained as classical risk models in a Markovian environment. Astin Bulletin 14, 23–43.Google Scholar
  14. [14]
    Reinhard, J. M. andSnoussi, M. (2000): The probability of ruin in a discrete semi Markov risk model. Blätter der Deutschen Gesellschaft für Versicherungsmathematik XXIV, 477–490.Google Scholar
  15. [15]
    Reinhard, J. M. andSnoussi, M. (2001a): On the distribution of the surplus prior to ruin in a discrete semi Markov risk model. To appear in Astin Bulletin.Google Scholar
  16. [16]
    Reinhard, J. M. andSnoussi, M. (2001b): The severity of ruin in a discrete semi-Markov risk model. To appear in Commun. Statist. — Stochastic Models.Google Scholar
  17. [17]
    Schmidli, H. (1999): On the distribution of the surplus prior and at ruin. Astin Bulletin, 29, 227–244.MATHCrossRefGoogle Scholar
  18. [18]
    Snoussi, M. (1998): The severity of ruin in the Markov-Modulated risk models. Proceedings of the 2nd International symposium on Semi-Markov Models: Theory and Applications. Ed. by J. Janssen and N. Limnios, Compiegne, 1998, 377–382.Google Scholar
  19. [19]
    Willmot, G. E. andLin, X. S. (1998): Exact and approximate properties of the distribution of surplus before and after ruin. Insurance: Mathematics and Economics 23, 91–110.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© DAV/DGVFM 2002

Authors and Affiliations

  • Mohammed Snoussi
    • 1
  1. 1.Brüssel

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