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Antimonotonicity for preference axioms: the natural counterpart to comonotonicity

Author

Listed:
  • Principi, Giulio

    (Department of Economics, New York University)

  • Wakker, Peter P.

    (School of Economics, Erasmus University Rotterdam)

  • Wang, Ruodu

    (Department of Statistics and Actuarial Science, University of Waterloo)

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.

Suggested Citation

  • Principi, Giulio & Wakker, Peter P. & Wang, Ruodu, 0. "Antimonotonicity for preference axioms: the natural counterpart to comonotonicity," Theoretical Economics, Econometric Society.
    • Handle: RePEc:the:publsh:5799
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    Keywords

    Comonotonicity; bookmaking; hedging; subjective expected utility; ambiguity aversion;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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