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A nonsmooth approach to nonexpected utility theory under risk

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  • Chatterjee, Kalyan
  • Vijay Krishna, R.

Abstract

We consider concave and Lipschitz continuous preference functionals over monetary lotteries. We show that they possess an envelope representation, as the minimum of a bounded family of continuous vN-M preference functionals. This allows us to use an envelope theorem to show that results from local utility analysis still hold in our setting, without any further differentiability assumptions on the preference functionals. Finally, we provide an axiomatisation of a class of concave preference functionals that are Lipschitz.

Suggested Citation

  • Chatterjee, Kalyan & Vijay Krishna, R., 2011. "A nonsmooth approach to nonexpected utility theory under risk," Mathematical Social Sciences, Elsevier, vol. 62(3), pages 166-175.
    • Handle: RePEc:eee:matsoc:v:62:y:2011:i:3:p:166-175
    DOI: 10.1016/j.mathsocsci.2011.08.001
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    References listed on IDEAS

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    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. Chateauneuf, Alain & Cohen, Michele, 1994. "Risk Seeking with Diminishing Marginal Utility in a Non-expected Utility Model," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 77-91, July.
    3. Machina, Mark J., 1984. "Temporal risk and the nature of induced preferences," Journal of Economic Theory, Elsevier, vol. 33(2), pages 199-231, August.
    4. D. Gale, 1967. "A Geometric Duality Theorem with Economic Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 19-24.
    5. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
    6. Mas-Colell, Andreu, 1977. "The Recoverability of Consumers' Preferences from Market Demand Behavior," Econometrica, Econometric Society, vol. 45(6), pages 1409-1430, September.
    7. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    8. Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, vol. 54(5), pages 1039-1053, September.
    9. Fabio Maccheroni, 2002. "Maxmin under risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 823-831.
    10. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    11. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    12. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    13. Keeney,Ralph L. & Raiffa,Howard, 1993. "Decisions with Multiple Objectives," Cambridge Books, Cambridge University Press, number 9780521438834.
    14. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    15. Safra, Zvi & Segal, Uzi, 1998. "Constant Risk Aversion," Journal of Economic Theory, Elsevier, vol. 83(1), pages 19-42, November.
    16. Hong, Chew Soo & Nishimura, Naoko, 1992. "Differentiability, comparative statics, and non-expected utility preferences," Journal of Economic Theory, Elsevier, vol. 56(2), pages 294-312, April.
    17. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-1119, July.
    18. Rader, Trout, 1972. "Theory of Microeconomics," Elsevier Monographs, Elsevier, edition 1, number 9780125750509.
    19. Haluk Ergin & Todd Sarver, 2010. "A Unique Costly Contemplation Representation," Econometrica, Econometric Society, vol. 78(4), pages 1285-1339, July.
    20. Edward E. Schlee, 2001. "The Value of Information in Efficient Risk-Sharing Arrangements," American Economic Review, American Economic Association, vol. 91(3), pages 509-524, June.
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    Cited by:

    1. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    2. Olivier Morand & Kevin Reffett & Suchismita Tarafdar, 2018. "Generalized Envelope Theorems: Applications to Dynamic Programming," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 650-687, March.

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