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

Risk aversion for nonsmooth utility functions

  • Würth, Andreas
  • Schumacher, J.M.

Abstract This paper generalizes the notion of risk aversion for functions which are not necessarily differentiable nor strictly concave. Using an approach based on superdifferentials, we define the notion of a risk aversion measure, from which the classical absolute as well as relative risk aversion follows as a Radon-Nikodym derivative if it exists. Using this notion, we are able to compare risk aversions for nonsmooth utility functions, and to extend a classical result of Pratt to the case of nonsmooth utility functions. We prove how relative risk aversion is connected to a super-power property of the function. Furthermore, we show how boundedness of the relative risk aversion translates to the corresponding property of the conjugate function. We propose also a weaker ordering of the risk aversion, referred to as essential bounds for the risk aversion, which requires only that bounds of the (absolute or relative) risk aversion hold up to a certain tolerance.

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 Journal of Mathematical Economics.

Volume (Year): 47 (2011)
Issue (Month): 2 (March)
Pages: 109-128

in new window

Handle: RePEc:eee:mateco:v:47:y:2011:i:2:p:109-128
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. Zhegal, Amina & Touzi, Nizar & Bouchard, Bruno, 2004. "Dual Formulation of the Utility Maximization Problem : the case of Nonsmooth Utility," Economics Papers from University Paris Dauphine 123456789/1531, Paris Dauphine University.
  2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  3. Lars Nielsen, 2005. "Monotone risk aversion," Economic Theory, Springer, vol. 25(1), pages 203-215, 01.
  4. Ariel Rubinstein, 2006. "Lecture Notes in Microeconomic Theory," Online economics textbooks, SUNY-Oswego, Department of Economics, number gradmicro1.
  5. B. Bouchard & N. Touzi & A. Zeghal, 2004. "Dual formulation of the utility maximization problem: the case of nonsmooth utility," Papers math/0405290,
  6. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
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:mateco:v:47:y:2011:i:2:p:109-128. 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.