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Greater parametric downside risk aversion

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  • Keenan, Donald C.
  • Snow, Arthur

Abstract

We show that, just as an expected utility maximizer with utility function u responds to a compensated increase in risk by adjusting a control variable to reduce the degree of risk aversion measured by the Arrow–Pratt index Ru=−u′′∕u′ (Diamond & Stiglitz, 1974), so the response to a compensated increase in downside risk entails adjusting the control to reduce the degree of downside risk aversion measured by the Schwarzian Su=u′′′∕u′−(3∕2)Ru2. We also show that, ceteris paribus, increases in Su and in Ru result in reduced exposure to downside risk and, therefore, greater demand for self-protection activities that reduce downside risk to future income. An increase from Su to Sv is characterized by downside risk-averse transformations of utility everywhere along a path from u to v, which together constitute what we define to be a parametric increase in downside risk aversion. These parametric increases yield comparative statics predictions not true if v is simply a downside risk-averse transformation of u, and predictions for incremental changes in risk preferences can be extended immediately to global changes.

Suggested Citation

  • Keenan, Donald C. & Snow, Arthur, 2017. "Greater parametric downside risk aversion," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 119-128.
  • Handle: RePEc:eee:mateco:v:71:y:2017:i:c:p:119-128
    DOI: 10.1016/j.jmateco.2017.05.002
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    References listed on IDEAS

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    Cited by:

    1. Keenan, Donald C. & Snow, Arthur, 2022. "Reversibly greater downside risk aversion by a prudence-based measure," Economics Letters, Elsevier, vol. 210(C).
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    3. 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.

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