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On Finite-Time Ruin Probabilities for Classical Risk Models

Listed author(s):
  • Claude Lefèvre


    (ULB - Département de Mathématique [Bruxelles] - ULB - Université Libre de Bruxelles [Bruxelles])

  • Stéphane Loisel


    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1)

This paper is concerned with the problem of ruin in the classical compound binomial and compound Poisson risk models. Our primary purpose is to extend to those models an exact formula derived by Picard and Lefèvre (1997) for the probability of (non-)ruin within finite time. First, a standard method based on the ballot theorem and an argument of Seal-type provides an initial (known) formula for that probability. Then, a concept of pseudo-distributions for the cumulated claim amounts, combined with some simple implications of the ballot theorem, leads to the desired formula. Two expressions for the (non-)ruin probability over an infinite horizon are also deduced as corollaries. Finally, an illustration within the framework of Solvency II is briefly presented.

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Paper provided by HAL in its series Post-Print with number hal-00168958.

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Date of creation: Jan 2008
Publication status: Published in Scandinavian Actuarial Journal, Taylor & Francis (Routledge), 2008, 2008 (1), pp.41-60. 〈10.1080/03461230701766882〉
Handle: RePEc:hal:journl:hal-00168958
DOI: 10.1080/03461230701766882
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  1. Rulliere, Didier & Loisel, Stephane, 2004. "Another look at the Picard-Lefevre formula for finite-time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 187-203, October.
  2. Loisel, Stéphane & Mazza, Christian & Rullière, Didier, 2008. "Robustness analysis and convergence of empirical finite-time ruin probabilities and estimation risk solvency margin," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 746-762, April.
  3. Willmot, Gordon E., 1993. "Ruin probabilities in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 12(2), pages 133-142, April.
  4. Cheng, Shixue & Gerber, Hans U. & Shiu, Elias S. W., 2000. "Discounted probabilities and ruin theory in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 239-250, May.
  5. Gerber, Hans U., 1988. "Mathematical Fun with the Compound Binomial Process," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 18(02), pages 161-168, November.
  6. De Vylder, F. Etienne & Goovaerts, Marc J., 1999. "Explicit finite-time and infinite-time ruin probabilities in the continuous case," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 155-172, May.
  7. Dickson, D.C.M., 1999. "On Numerical Evaluation of Finite Time Survival Probabilities," British Actuarial Journal, Cambridge University Press, vol. 5(03), pages 575-584, August.
  8. Konstantopoulos, Takis, 1995. "Ballot theorems revisited," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 331-338, September.
  9. Ignatov, Zvetan G. & Kaishev, Vladimir K. & Krachunov, Rossen S., 2001. "An improved finite-time ruin probability formula and its Mathematica implementation," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 375-386, December.
  10. De Vylder, F. & Goovaerts, M. J., 1988. "Recursive calculation of finite-time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 7(1), pages 1-7, January.
  11. Cardoso, Rui M. R. & R. Waters, Howard, 2003. "Recursive calculation of finite time ruin probabilities under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 659-676, December.
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