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Prudence, temperance, edginess, and risk apportionment as decreasing sensitivity to detrimental changes

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  • Denuit, Michel
  • Rey, Béatrice
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    Abstract

    This paper shows that the notions of prudence, temperance, edginess, and, more generally, risk apportionment of any degree are the consequences of the natural idea that the sensitivity to detrimental changes should decrease with initial wealth. In the setting of Epstein and Tanny (1980), this turns out to be equivalent to the supermodularity of the expected utility for some specific 4-state lotteries.

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    Bibliographic Info

    Article provided by Elsevier in its journal Mathematical Social Sciences.

    Volume (Year): 60 (2010)
    Issue (Month): 2 (September)
    Pages: 137-143

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    Handle: RePEc:eee:matsoc:v:60:y:2010:i:2:p:137-143

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    Web page: http://www.elsevier.com/locate/inca/505565

    Related research

    Keywords: Expected utility Wealth effect Supermodularity Stochastic dominance;

    References

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    1. Louis Eeckhoudt & Harris Schlesinger & Ilia Tsetlin, 2008. "Apportioning of Risks via Stochastic Dominance," CESifo Working Paper Series 2467, CESifo Group Munich.
    2. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    3. Caballe, Jordi & Pomansky, Alexey, 1996. "Mixed Risk Aversion," Journal of Economic Theory, Elsevier, vol. 71(2), pages 485-513, November.
    4. Dhaene, Jan & Denuit, Michel, 1999. "The safest dependence structure among risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 11-21, September.
    5. Jones-Lee, Michael W, 1974. "The Value of Changes in the Probability of Death or Injury," Journal of Political Economy, University of Chicago Press, vol. 82(4), pages 835-49, July/Aug..
    6. Doherty, Neil A & Schlesinger, Harris, 1983. "Optimal Insurance in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 91(6), pages 1045-54, December.
    7. BLEICHRODT, Han & EECKHOUDT, Louis, . "Saving under rank-dependent utility," CORE Discussion Papers RP -1752, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Miles S. Kimball, 1989. "Precautionary Saving in the Small and in the Large," NBER Working Papers 2848, National Bureau of Economic Research, Inc.
    9. Jindapon, Paan & Neilson, William S., 2007. "Higher-order generalizations of Arrow-Pratt and Ross risk aversion: A comparative statics approach," Journal of Economic Theory, Elsevier, vol. 136(1), pages 719-728, September.
    10. Marie-Cécile Fagart & Bernard Sinclair-Desgagné, 2007. "Ranking Contingent Monitoring Systems," Management Science, INFORMS, vol. 53(9), pages 1501-1509, September.
    11. repec:cor:louvrp:2207 is not listed on IDEAS
    12. Denuit, Michel & Vylder, Etienne De & Lefevre, Claude, 1999. "Extremal generators and extremal distributions for the continuous s-convex stochastic orderings," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 201-217, May.
    13. Chiu, W.Henry, 2005. "Degree of downside risk aversion and self-protection," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 93-101, February.
    14. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279.
    15. Lajeri-Chaherli, Fatma, 2004. "Proper prudence, standard prudence and precautionary vulnerability," Economics Letters, Elsevier, vol. 82(1), pages 29-34, January.
    16. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
    17. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-23, September.
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    Citations

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    Cited by:
    1. Denuit, Michel & Rey, Béatrice, 2013. "Another look at risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 335-343.
    2. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    3. 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.
    4. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART - LERECO 14-01, INRA UMR SMART.
    5. David Crainich & Louis Eeckhoudt & Olivier Le Courtois, 2013. "An index of (absolute) correlation aversion: theory and some implications," Working Papers 2013-ECO-12, IESEG School of Management.

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