Duality mappings for the theory of risk aversion with vector outcomes
We consider a decision-making environment with an outcome space that is a convex and compact subset of a vector space belonging to a general class of such spaces. Given this outcome space, we de¯ne gen- eral classes of (a) risk averse von Neumann-Morgenstern utility func- tions de¯ned over the outcome space, (b) multi-valued mappings that yield the certainty equivalent outcomes corresponding to a lottery, (c) multi-valued mappings that yield the risk premia corresponding to a lottery, and (d) multi-valued mappings that yield the acceptance set of lotteries corresponding to an outcome. Our duality results establish that the usual mappings that generate (b), (c) and (d) from (a) are bi- jective. We apply these results to the problem of computing the value of ¯nancial assets to a risk averse decision-maker and show that this value will always be less than the arbitrage-free valuation.
|Date of creation:||Aug 2007|
|Date of revision:|
|Contact details of provider:|| Postal: Delhi 110 007|
Phone: (011) 27667005
Fax: (011) 27667159
Web page: http://www.cdedse.org/
More information through EDIRC
|Order Information:|| Web: http://www.cdedse.org/ Email: |
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.:
- Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
- Duncan, George T, 1977. "A Matrix Measure of Multivariate Local Risk Aversion," Econometrica, Econometric Society, vol. 45(4), pages 895-903, May.
- Grant, Simon & Kajii, Atsushi & Polak, Ben, 1992. "Many good risks: An interpretation of multivariate risk and risk aversion without the Independence axiom," Journal of Economic Theory, Elsevier, vol. 56(2), pages 338-351, April.
- Levy, Haim & Levy, Azriel, 1991. "Arrow-Pratt Measures of Risk Aversion: The Multivariate Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(4), pages 891-98, November.
- Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
- Juan Martínez-Legaz & John Quah, 2007. "A contribution to duality theory, applied to the measurement of risk aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(2), pages 337-362, February.
- Richard E. Kihlstrom & Leonard J. Mirman, 1981. "Constant, Increasing and Decreasing Risk Aversion with Many Commodities," Review of Economic Studies, Oxford University Press, vol. 48(2), pages 271-280.
- Grant, Simon & Kajii, Atsushi & Polak, Ben, 1992. "Many good choice Axioms: When can many-good lotteries be treated as money lotteries?," Journal of Economic Theory, Elsevier, vol. 56(2), pages 313-337, April.
When requesting a correction, please mention this item's handle: RePEc:cde:cdewps:160. 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: (Sanjeev Sharma)
If references are entirely missing, you can add them using this form.