Paper: arXiv 2501.13143

Authors: Mücahit Aygün, Roger J. A. Laeven, Mitja Stadje

Abstract

We introduce a model-free preference under ambiguity, as a primitive trait of behavior, which we apply once as well as repeatedly. Its single and double application yield simple, easily interpretable definitions of ambiguity aversion and ambiguity prudence. We derive their implications within canonical models for decision under risk and ambiguity. We establish in particular that our new definition of ambiguity prudence is equivalent to a positive third derivative of: (i) the capacity in the Choquet expected utility model, (ii) the dual conjugate of the divergence function under variational divergence preferences and (iii) the ambiguity attitude function in the smooth ambiguity model. We show that our definition of ambiguity prudent behavior may be naturally linked to an optimal insurance problem under ambiguity.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework establishing model-free higher-order ambiguity attitudes and connecting them to capacity derivatives across various decision models. However, it is entirely theoretical with no empirical data or backtesting, placing it firmly in the ‘Lab Rats’ quadrant.

Research Flowchart

  flowchart TD
    A[Research Goal: Define Higher-Order Ambiguity Attitudes] --> B[Introduce Primitive Trait for Single & Double Ambiguity Application]
    B --> C[Derive Model-Free Definitions: Ambiguity Aversion & Prudence]
    C --> D[Apply Framework to Canonical Decision Models]
    D --> E[Mathematical Derivation of Equivalent Third Derivatives]
    E --> F[Findings: Equivalent to Positive 3rd Derivative in CEU, Variational & Smooth Models]
    E --> G[Outcome: Link Ambiguity Prudence to Optimal Insurance Decisions]

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2 of 64 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.