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The values of relative risk aversion and prudence: A context-free interpretation

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  • EECKHOUDT, Louis
  • ETNER, Johanna
  • SCHROYEN, Fred

Abstract

In this paper we apply to multiplicative lotteries the idea of preference for "harm disaggregation" that was used for additive lotteries in order to interpret the signs of successive derivatives of a utility function. In this way, we can explain in general terms why the values of the coefficients of relative risk aversion and relative prudence are usually compared respectively to 1 and 2. We also show how these values partition the sets of risk averse and/or prudent decision makers into two subgroups.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number -2162.

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Handle: RePEc:cor:louvrp:-2162

Note: In : Mathematical Social Sciences, 58, 1-7, 2009
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  1. Cheng, Hsueh-Cheng & Magill, Michael J P & Shafer, Wayne J, 1987. "Some Results on Comparative Statics under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(2), pages 493-507, June.
  2. Mitchell, Douglas W, 1994. "Relative Risk Aversion with Arrow-Debreu Securities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(1), pages 257-58, February.
  3. Louis Eeckhoudt & Harris Schlesinger, 2005. "Putting Risk in its Proper Place," CESifo Working Paper Series 1462, CESifo Group Munich.
  4. Peter C. Fishburn & R. Burr Porter, 1976. "Optimal Portfolios with One Safe and One Risky Asset: Effects of Changes in Rate of Return and Risk," Management Science, INFORMS, INFORMS, vol. 22(10), pages 1064-1073, June.
  5. Donald Meyer & Jack Meyer, 2005. "Relative Risk Aversion: What Do We Know?," Journal of Risk and Uncertainty, Springer, Springer, vol. 31(3), pages 243-262, December.
  6. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, Econometric Society, vol. 58(1), pages 53-73, January.
  7. Choi, E. K. & Menezes, C. F., 1985. "On the magnitude of relative risk aversion," Economics Letters, Elsevier, Elsevier, vol. 18(2-3), pages 125-128.
  8. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2003. "Multiplicative Background Risk," CoFE Discussion Paper, Center of Finance and Econometrics, University of Konstanz 03-05, Center of Finance and Econometrics, University of Konstanz.
  9. Chiu, W.Henry & Madden, Paul, 2007. "Crime, punishment, and background risks," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 62(4), pages 543-555, April.
  10. Choi, Gyemyung & Kim, Iltae & Snow, Arthur, 2001. "Comparative Statics Predictions for Changes in Uncertainty in the Portfolio and Savings Problems," Bulletin of Economic Research, Wiley Blackwell, vol. 53(1), pages 61-72, January.
  11. White, Lucy, 2008. "Prudence in bargaining: The effect of uncertainty on bargaining outcomes," Games and Economic Behavior, Elsevier, Elsevier, vol. 62(1), pages 211-231, January.
  12. Hadar, Josef & Seo, Tae Kun, 1990. "The Effects of Shifts in a Return Distribution on Optimal Portfolios," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 721-36, August.
  13. Hahn, F H, 1970. "Savings and Uncertainty," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 37(1), pages 21-24, January.
  14. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, Elsevier, vol. 3(1), pages 66-84, March.
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Cited by:
  1. Fred Schroyen & Adekola Oyenuga, 2011. "Optimal pricing and capacity choice for a public service under risk of interruption," Journal of Regulatory Economics, Springer, Springer, vol. 39(3), pages 252-272, June.
  2. Jingyuan Li, 2012. "Precautionary saving in the presence of labor income and interest rate risks," Journal of Economics, Springer, Springer, vol. 106(3), pages 251-266, July.
  3. Denuit, Michel & Rey, Béatrice, 2013. "Another look at risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 335-343.
  4. W. Chiu & Louis Eeckhoudt & Beatrice Rey, 2012. "On relative and partial risk attitudes: theory and implications," Economic Theory, Springer, Springer, vol. 50(1), pages 151-167, May.
  5. Wang, Jianli & Li, Jingyuan, 2010. "Multiplicative risk apportionment," Mathematical Social Sciences, Elsevier, Elsevier, vol. 60(1), pages 79-81, July.
  6. Michel Denuit & Béatrice Rey, 2014. "Benchmark values for higher order coefficients of relative risk aversion," Theory and Decision, Springer, Springer, vol. 76(1), pages 81-94, January.
  7. Noussair, C.N. & Trautmann, S.T. & Kuilen, G. van de, 2011. "Higher Order Risk Attitudes, Demographics, and Financial Decisions," Discussion Paper, Tilburg University, Center for Economic Research 2011-055, Tilburg University, Center for Economic Research.
  8. Octave Jokung, 2013. "Changes in multiplicative background risk and risk-taking behavior," Theory and Decision, Springer, Springer, vol. 74(1), pages 127-149, January.
  9. Eichner, Thomas & Wagener, Andreas, 2011. "Increases in skewness and three-moment preferences," Mathematical Social Sciences, Elsevier, Elsevier, vol. 61(2), pages 109-113, March.
  10. Jokung, Octave, 2013. "Monotonicity of asset price toward higher changes in risk," Economics Letters, Elsevier, Elsevier, vol. 118(1), pages 195-198.
  11. Courbage, Christophe & Rey, Béatrice, 2012. "Priority setting in health care and higher order degree change in risk," Journal of Health Economics, Elsevier, Elsevier, vol. 31(3), pages 484-489.

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