IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes

Listed author(s):
  • Stéphane Loisel


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

  • Christian Mazza


    (Département de Mathématiques - Université de Fribourg)

  • Didier Rullière


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

The classical risk model is considered and a sensitivity analysis of finite-time ruin probabilities is carried out. We prove the weak convergence of a sequence of empirical finite-time ruin probabilities. So-called partly shifted risk processes are introduced, and used to derive an explicit expression of the asymptotic variance of the considered estimator. This provides a clear representation of the influence function associated with finite time ruin probabilities, giving a useful tool to quantify estimation risk according to new regulations.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by HAL in its series Post-Print with number hal-00168716.

in new window

Date of creation: Dec 2009
Publication status: Published in Insurance Mathematics and Economics, 2009, 45 (3), pp.374-381. <10.1016/j.insmatheco.2009.08.003>
Handle: RePEc:hal:journl:hal-00168716
DOI: 10.1016/j.insmatheco.2009.08.003
Note: View the original document on HAL open archive server:
Contact details of provider: Web page:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

in new window

  1. Croux, Kristof & Veraverbeke, Noel, 1990. "Nonparametric estimators for the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 127-130, September.
  2. Stéphane Loisel & Nicolas Privault, 2009. "Sensitivity analysis and density estimation for finite-time ruin probabilities," Post-Print hal-00201347, HAL.
  3. Stéphane Loisel & Claude Lefèvre, 2009. "Finite-Time Ruin Probabilities for Discrete, Possibly Dependent, Claim Severities," Post-Print hal-00201377, HAL.
  4. Hipp, Christian, 1989. "Estimators and Bootstrap Confidence Intervals for Ruin Probabilities," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 19(01), pages 57-70, April.
  5. Claude Lefèvre & Stéphane Loisel, 2008. "On Finite-Time Ruin Probabilities for Classical Risk Models," Post-Print hal-00168958, HAL.
  6. Stéphane Loisel & Christian Mazza & Didier Rullière, 2008. "Robustness analysis and convergence of empirical finite-time ruin probabilities and estimation risk solvency margin," Post-Print hal-00168714, HAL.
  7. Marceau, Etienne & Rioux, Jacques, 2001. "On robustness in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 167-185, October.
  8. Christian Mazza & Didier Rullière, 2004. "A link between wave governed random motions and ruin processes," Post-Print hal-00412977, HAL.
  9. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 12(01), pages 22-26, June.
  10. 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.
  11. Frees, Edward W., 1986. "Nonparametric Estimation of the Probability of Ruin," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 16(S1), pages 81-90, April.
  12. Biard, Romain & Lefèvre, Claude & Loisel, Stéphane, 2008. "Impact of correlation crises in risk theory: Asymptotics of finite-time ruin probabilities for heavy-tailed claim amounts when some independence and stationarity assumptions are relaxed," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 412-421, December.
  13. Picard, Philippe & Lefevre, Claude, 1998. "The moments of ruin time in the classical risk model with discrete claim size distribution," Insurance: Mathematics and Economics, Elsevier, vol. 23(2), pages 157-172, November.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00168716. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.