IDEAS home Printed from
MyIDEAS: Login to save this article or follow this journal

On cross-risk vulnerability

  • Malevergne, Y.
  • Rey, B.

We introduce the notion of cross-risk vulnerability to generalize the concept of risk vulnerability introduced by Gollier and Pratt [Gollier, C., Pratt, J.W. 1996. Risk vulnerability and the tempering effect of background risk. Econometrica 64, 1109-1124]. While risk vulnerability captures the idea that the presence of an unfair financial background risk should make risk-averse individuals behave in a more risk-averse way with respect to an independent financial risk, cross-risk vulnerability extends this idea to the impact of a non-financial background risk on the financial risk. It provides an answer to the question of the impact of a background risk on the optimal coinsurance rate and on the optimal deductible level. We derive necessary and sufficient conditions for a bivariate utility function to exhibit cross-risk vulnerability both toward an actuarially neutral background risk and toward an unfair background risk. We also analyze the question of the sub-additivity of risk premia and show to what extent cross-risk vulnerability provides an answer.

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: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 45 (2009)
Issue (Month): 2 (October)
Pages: 224-229

in new window

Handle: RePEc:eee:insuma:v:45:y:2009:i:2:p:224-229
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.:

as in new window
  1. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-54, January.
  2. Bleichrodt, Han & Crainich, David & Eeckhoudt, Louis, 2003. "Comorbidities and the willingness to pay for health improvements," Journal of Public Economics, Elsevier, vol. 87(11), pages 2399-2406, October.
  3. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
  4. Thomas Eichner & Andreas Wagener, 2003. "Variance Vulnerability, Background Risks, and Mean-Variance Preferences," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 28(2), pages 173-184, December.
  5. Israel Finkelshtain & James A. Chalfant, 1993. "Portfolio Choices in the Presence of Other Risks," Management Science, INFORMS, vol. 39(8), pages 925-936, August.
  6. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
  7. EECKHOUDT, Louis & GOLLIER, Christian, . "Which shape for the cost curve of risk?," CORE Discussion Papers RP 1583, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. BÈatrice Rey, 2003. "Total and partial Bivariate Risk Premia: An Extension," Theory and Decision, Springer, vol. 55(1), pages 59-69, 08.
  9. Doherty, Neil A & Schlesinger, Harris, 1983. "The Optimal Deductible for an Insurance Policy When Initial Wealth Is Random," The Journal of Business, University of Chicago Press, vol. 56(4), pages 555-65, October.
  10. Scott F. Richard, 1975. "Multivariate Risk Aversion, Utility Independence and Separable Utility Functions," Management Science, INFORMS, vol. 22(1), pages 12-21, September.
  11. Doherty, Neil A. & Schlesinger, Harris, 1986. "A note on risk premiums with random initial wealth," Insurance: Mathematics and Economics, Elsevier, vol. 5(3), pages 183-185, July.
  12. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2006. "Multiplicative Background Risk," Management Science, INFORMS, vol. 52(1), pages 146-153, January.
  13. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
  14. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-23, September.
  15. Menegatti, Mario, 2001. "On the Conditions for Precautionary Saving," Journal of Economic Theory, Elsevier, vol. 98(1), pages 189-193, May.
  16. Louis Eeckhoudt & Harris Schlesinger, 2005. "Putting Risk in its Proper Place," CESifo Working Paper Series 1462, CESifo Group Munich.
  17. Kischka, Peter, 1988. "Aspects of optimal insurance demand when there are uninsurable risks," Insurance: Mathematics and Economics, Elsevier, vol. 7(1), pages 9-14, January.
  18. Safra, Zvi & Segal, Uzi, 1998. "Constant Risk Aversion," Journal of Economic Theory, Elsevier, vol. 83(1), pages 19-42, November.
  19. Günter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 2005. "Incremental Risk Vulnerability," CoFE Discussion Paper 05-08, Center of Finance and Econometrics, University of Konstanz.
  20. John Quiggin, 2003. "Background risk in generalized expected utility theory," Economic Theory, Springer, vol. 22(3), pages 607-611, October.
  21. EECKHOUDT, Louis & Christian GOLLIER & Harris SCHLESINGER, 1994. "Changes in Background Risk and Risk Taking Behavior," Working Papers 005, Risk and Insurance Archive.
  22. Kihlstrom, Richard E & Romer, David & Williams, Steve, 1981. "Risk Aversion with Random Initial Wealth," Econometrica, Econometric Society, vol. 49(4), pages 911-20, June.
  23. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
  24. Thomas Eichner, 2008. "Mean Variance Vulnerability," Management Science, INFORMS, vol. 54(3), pages 586-593, March.
  25. Sloan, Frank A. & Kip Viscusi, W. & Chesson, Harrell W. & Conover, Christopher J. & Whetten-Goldstein, Kathryn, 1998. "Alternative approaches to valuing intangible health losses: the evidence for multiple sclerosis1," Journal of Health Economics, Elsevier, vol. 17(4), pages 475-497, August.
  26. Nachman, David C., 1982. "Preservation of "more risk averse" under expectations," Journal of Economic Theory, Elsevier, vol. 28(2), pages 361-368, December.
  27. Doherty, Neil A & Schlesinger, Harris, 1983. "Optimal Insurance in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 91(6), pages 1045-54, December.
  28. Christophe Courbage, 2001. "On Bivariate Risk Premia," Theory and Decision, Springer, vol. 50(1), pages 29-34, February.
  29. H. Bleichrodt & L. Eeckhoudt, 2006. "Survival risks, intertemporal consumption, and insurance: The case of distorted probabilities," Post-Print hal-00199632, HAL.
  30. Quiggin, John & Chambers, Robert G, 1998. "Risk Premiums and Benefit Measures for Generalized-Expected-Utility Theories," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 121-37, November.
  31. Chiu, W.Henry, 2005. "Degree of downside risk aversion and self-protection," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 93-101, February.
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:eee:insuma:v:45:y:2009:i:2:p:224-229. 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: (Zhang, Lei)

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.