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An axiomatization of the smooth ambiguity model using differentiability

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  • Giraud, Raphaël

Abstract

The smooth ambiguity model (Klibanoff et al., 2005) or second-order subjective expected utility (SOSEU) model (Nau, 2006; Seo, 2009; Giraud, 2014) has two characteristics that contribute to its success: it is an iterated expected utility and, under certain conditions, it is smooth. These characteristics allow for the use of standard analytical techniques from expected utility theory, including optimization calculus. In this paper, we utilize the continuous differentiability (C1) of the SOSEU functional to offer an axiomatic characterization of this model. First, we define C1 preferences and provide a representation for them. Then, assuming that preferences are C1, the primary axiom that delivers the iterated expected utility form essentially states that if decision makers are more sensitive to perturbations of one portfolio of assets than another one when the probability distribution is known, then they are still more sensitive when it is not.

Suggested Citation

  • Giraud, Raphaël, 2026. "An axiomatization of the smooth ambiguity model using differentiability," Journal of Mathematical Economics, Elsevier, vol. 125(C).
    • Handle: RePEc:eee:mateco:v:125:y:2026:i:c:s0304406826000595
    DOI: 10.1016/j.jmateco.2026.103271
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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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