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Ross risk vulnerability for introductions and changes in background risk

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  • Keenan, Donald C.
  • Snow, Arthur

Abstract

We present two theorems that provide necessary and sufficient conditions for an expected utility maximizer to become more risk averse in the sense of Ross with respect to bearing a foreground risk after the introduction of any independent fair or unfair additive background risk. We call these decision makers Ross risk vulnerable, and show that Ross decreasing absolute risk aversion and Ross decreasing absolute prudence are jointly sufficient for Ross risk vulnerability. Restrictions on utility necessary and sufficient for Ross risk vulnerability with respect to stochastic dominance deteriorations of an existing background risk are also presented. Our analysis concludes with applications of Ross risk vulnerability.

Suggested Citation

  • Keenan, Donald C. & Snow, Arthur, 2012. "Ross risk vulnerability for introductions and changes in background risk," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 197-206.
  • Handle: RePEc:eee:mateco:v:48:y:2012:i:4:p:197-206
    DOI: 10.1016/j.jmateco.2012.04.003
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    Cited by:

    1. Wang, Jianli & Li, Jingyuan, 2014. "Decreasing Ross risk aversion: Higher-order generalizations and implications," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 136-142.
    2. Denuit, Michel M. & Eeckhoudt, Louis & Schlesinger, Harris, 2013. "When Ross meets Bell: The linex utility function," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 177-182.
    3. Maddalena Ferranna, 2017. "Does Inefficient Risk Sharing Increase Public Self-Protection?," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 42(1), pages 59-85, March.

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