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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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    Cited by:

    1. Corrao, Roberto & Fudenberg, Drew & Levine, David K., 2024. "On concave functions over lotteries," Journal of Mathematical Economics, Elsevier, vol. 110(C).
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    3. 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.
    4. Sadowski, Philipp & Sarver, Todd, 2024. "Adaptive preferences: An evolutionary model of non-expected utility and ambiguity aversion," Journal of Economic Theory, Elsevier, vol. 218(C).

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