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Apportioning of Risks via Stochastic Dominance

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  • Louis Eeckhoudt
  • Harris Schlesinger
  • Ilia Tsetlin

Abstract

Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable Xi dominates Yi via ith-order stochastic dominance for i = M,N. We show that the 50-50 lottery [XN + YM, YN + XM] dominates the lottery [XN + XM, YN + YM] 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

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2467.

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Date of creation: 2008
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Handle: RePEc:ces:ceswps:_2467

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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. A. Mantovi, 2013. "Mapping completely proper rationality," Economics Department Working Papers 2013-EP01, Department of Economics, Parma University (Italy).
  2. Michel Denuit & Liqun Liu, 2014. "Decreasing higher-order absolute risk aversion and higher-degree stochastic dominance," Theory and Decision, Springer, Springer, vol. 76(2), pages 287-295, February.
  3. Wang, Jianli & Li, Jingyuan, 2010. "Multiplicative risk apportionment," Mathematical Social Sciences, Elsevier, Elsevier, vol. 60(1), pages 79-81, July.
  4. Denuit, Michel & Rey, Béatrice, 2010. "Prudence, temperance, edginess, and risk apportionment as decreasing sensitivity to detrimental changes," Mathematical Social Sciences, Elsevier, Elsevier, vol. 60(2), pages 137-143, September.
  5. Nocetti, Diego & Napp, Clotilde & Jouini, Elyès, 2012. "Economic Consequences of Nth-Degree Risk Increases and Nth-Degree Risk Attitudes," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/11094, Paris Dauphine University.
  6. 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.
  7. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART - LERECO, INRA UMR SMART 14-01, INRA UMR SMART.
  8. David Crainich & Louis Eeckhoudt & Alain Trannoy, 2013. "Even (Mixed) Risk Lovers Are Prudent," American Economic Review, American Economic Association, American Economic Association, vol. 103(4), pages 1529-35, June.
  9. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, Springer, vol. 47(2), pages 129-145, October.
  10. Menegatti, Mario, 2014. "New results on the relationship among risk aversion, prudence and temperance," European Journal of Operational Research, Elsevier, Elsevier, vol. 232(3), pages 613-617.
  11. Cary Deck & Harris Schlesinger, 2012. "Consistency of Higher Order Risk Preferences," CESifo Working Paper Series 4047, CESifo Group Munich.
  12. 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.
  13. Jokung, Octave, 2011. "Risk apportionment via bivariate stochastic dominance," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 448-452.
  14. Denuit, Michel M. & Eeckhoudt, Louis, 2010. "Stronger measures of higher-order risk attitudes," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(5), pages 2027-2036, September.
  15. Denuit, Michel & Rey, Béatrice, 2013. "Another look at risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 335-343.
  16. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2014. "Almost Stochastic Dominance for Risk-Averse and Risk-Seeking Investors," MPRA Paper 53347, University Library of Munich, Germany.

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