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Apportioning of risks via stochastic dominance

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  • Eeckhoudt, Louis
  • Schlesinger, Harris
  • Tsetlin, Ilia

Abstract

Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable dominates via ith-order stochastic dominance for i=M,N. We show that the 50-50 lottery dominates the lottery via (N+M)th-order stochastic dominance. The basic idea is that a decision maker exhibiting (N+M)th-order stochastic dominance preference will allocate the state-contingent lotteries in such a way as not to group the two "bad" lotteries in the same state, where "bad" is defined via ith-order stochastic dominance. In this way, we can extend and generalize existing results about risk attitudes. This lottery preference includes behavior exhibiting higher-order risk effects, such as precautionary effects and tempering effects.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 3 (May)
Pages: 994-1003

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:3:p:994-1003

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Downside risk Precautionary effects Prudence Risk apportionment Risk aversion Stochastic dominance Temperance;

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References

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Citations

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Cited by:
  1. Elyès Jouini & Clotilde Napp & Diego Nocetti, 2013. "Economic consequences of Nth-degree risk increases and Nth-degree risk attitudes," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 199-224, October.
  2. Menegatti, Mario, 2014. "New results on the relationship among risk aversion, prudence and temperance," European Journal of Operational Research, Elsevier, vol. 232(3), pages 613-617.
  3. Jokung, Octave, 2011. "Risk apportionment via bivariate stochastic dominance," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 448-452.
  4. Gollier, Christian & Hammitt, James & Treich, Nicolas, 2013. "Risk and Choice: A Research Saga," IDEI Working Papers 804, Institut d'Économie Industrielle (IDEI), Toulouse.
  5. Denuit, Michel & Rey, Béatrice, 2013. "Another look at risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 335-343.
  6. Denuit, Michel & Rey, Béatrice, 2010. "Prudence, temperance, edginess, and risk apportionment as decreasing sensitivity to detrimental changes," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 137-143, September.
  7. Xu, Guo & Wing-Keung, Wong & Lixing, Zhu, 2013. "Almost Stochastic Dominance for Risk-Averse and Risk-Seeking Investors," MPRA Paper 51744, University Library of Munich, Germany.
  8. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART - LERECO 14-01, INRA UMR SMART.
  9. Denuit, Michel M. & Eeckhoudt, Louis, 2010. "Stronger measures of higher-order risk attitudes," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2027-2036, September.
  10. A. Mantovi, 2013. "Mapping completely proper rationality," Economics Department Working Papers 2013-EP01, Department of Economics, Parma University (Italy).
  11. Michel Denuit & Liqun Liu, 2014. "Decreasing higher-order absolute risk aversion and higher-degree stochastic dominance," Theory and Decision, Springer, vol. 76(2), pages 287-295, February.
  12. David Crainich & Louis Eeckhoudt & Alain Trannoy, 2011. "Even (mixed) risk lovers are prudent," Working Papers 2011-ECO-05, IESEG School of Management.
  13. David Crainich & Louis Eeckhoudt & James K. Hammitt, 2013. "The Value of Risk Reduction: New Tools for an Old Problem," Working Papers 2013-ECO-13, IESEG School of Management.
  14. Cary Deck & Harris Schlesinger, 2012. "Consistency of Higher Order Risk Preferences," CESifo Working Paper Series 4047, CESifo Group Munich.
  15. Wang, Jianli & Li, Jingyuan, 2010. "Multiplicative risk apportionment," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 79-81, July.

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