Antimonotonicity for preference axioms: the natural counterpart to comonotonicity

Giulio Principi (), Peter Wakker and Ruodu Wang ()
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Giulio Principi: Department of Economics, New York University
Ruodu Wang: Department of Statistics and Actuarial Science, University of Waterloo

Theoretical Economics, Forthcoming

Abstract: Comonotonicity (``same variation'') of random variables minimizes hedging possibilities and has been widely used, e.g., in Gilboa and Schmeidler's ambiguity models. This paper investigates anticomonotonicity (``opposite variation''; abbreviated ``AC''), the natural counterpart to comonotonicity. It minimizes leveraging rather than hedging possibilities. Surprisingly, AC restrictions of several traditional axioms do not give new models. Instead, they strengthen the foundations of existing classical models: (a) linear functionals through Cauchy's equation; (b) Anscombe-Aumann expected utility; (c) as-if-risk-neutral pricing through no-arbitrage; (d) de Finetti's bookmaking foundation of Bayesianism using subjective probabilities; (e) risk aversion in Savage's subjective expected utility. In each case, our generalizations show where the critical tests of classical axioms lie: in the AC cases (maximal hedges). We next present examples where AC restrictions do essentially weaken existing axioms, and do provide new properties and new models.

Keywords: Comonotonicity; bookmaking; hedging; subjective expected utility; ambiguity aversion (search for similar items in EconPapers)
JEL-codes: C02 C60 D81 (search for similar items in EconPapers)
Date: 2024-12-16
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Related works:
Working Paper: Anticomonotonicity for Preference Axioms: The Natural Counterpart to Comonotonicity (2024)
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