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Bringing order to rankings of utility functions by strong increases in nth order aversion to risk

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  • Keenan, Donald C.
  • Snow, Arthur
Abstract
Rankings of utility functions generated by simple nth order risk-averse transformations are not partial orders, and therefore, do not yield reliable comparative statics predictions, except at the second order. Restrictions have been identified that rectify this deficiency at the third order concerning downside risk aversion: the strong order and the Schwarzian. We show that these concepts and their characterizations generalize to all higher orders of risk preference, the latter in two ways, pathwise (parametric) infinitesimal increases and n-monotone increases in aversion to risk, and we provide applications to intertemporal choice problems for self-protection and saving.

Suggested Citation

  • Keenan, Donald C. & Snow, Arthur, 2018. "Bringing order to rankings of utility functions by strong increases in nth order aversion to risk," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 35-44.
    • Handle: RePEc:eee:mateco:v:78:y:2018:i:c:p:35-44
    DOI: 10.1016/j.jmateco.2018.07.004
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    References listed on IDEAS

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    1. Menegatti, Mario, 2009. "Optimal prevention and prudence in a two-period model," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 393-397, November.
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    10. Donald C. Keenan & Arthur Snow, 2016. "Strong Increases in Downside Risk Aversion," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 41(2), pages 149-161, September.
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    Cited by:

    1. De Donno, Marzia & Menegatti, Mario, 2022. "On the relationship between comparisons of risk aversion of different orders," Journal of Mathematical Economics, Elsevier, vol. 102(C).

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