Risk aversion for nonsmooth utility functions
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.
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.:
- Ariel Rubinstein, 2006. "Lecture Notes in Microeconomic Theory," Online economics textbooks, SUNY-Oswego, Department of Economics, number gradmicro1.
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, December.
- Lars Tyge Nielsen, 2003.
"Monotone Risk Aversion,"
03-10, University of Copenhagen. Department of Economics.
- B. Bouchard & N. Touzi & A. Zeghal, 2004. "Dual formulation of the utility maximization problem: the case of nonsmooth utility," Papers math/0405290, arXiv.org.
- Mark J Machina, 1982.
""Expected Utility" Analysis without the Independence Axiom,"
Levine's Working Paper Archive
7650, David K. Levine.
- Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
- repec:dau:papers:123456789/1531 is not listed 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: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.