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When Ross meets Bell: The linex utility function

Listed author(s):
  • Denuit, Michel M.
  • Eeckhoudt, Louis
  • Schlesinger, Harris

At first glance, there would appear to be no relationship between Bell’s (1988) concept of one-switch utility functions and that of a stronger measure of risk aversion due to Ross (1981). We show however that specific assumptions about the behavior of the stronger measure of risk aversion also give rise to the linex utility function which belongs to the class of one-switch utility functions. In particular, this utility class is the only one that satisfies a stronger version of Kimball’s (1993) standard risk aversion over all levels of wealth. We apply our results to consider nth-degree deteriorations in background risk and their effect on risk taking behavior.

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File URL: http://www.sciencedirect.com/science/article/pii/S0304406813000086
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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 49 (2013)
Issue (Month): 2 ()
Pages: 177-182

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Handle: RePEc:eee:mateco:v:49:y:2013:i:2:p:177-182
DOI: 10.1016/j.jmateco.2013.01.006
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. Denuit, Michel M. & Eeckhoudt, Louis, 2013. "Improving your chances: A new result," Economics Letters, Elsevier, vol. 118(3), pages 475-477.
  2. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
  3. Menezes, Carmen F. & Wang, X.Henry, 2005. "Increasing outer risk," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 875-886, November.
  4. Modica, Salvatore & Scarsini, Marco, 2005. "A note on comparative downside risk aversion," Journal of Economic Theory, Elsevier, vol. 122(2), pages 267-271, June.
  5. 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.
  6. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1996. "Changes in Background Risk and Risk-Taking Behavior," Econometrica, Econometric Society, vol. 64(3), pages 683-689, May.
  7. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
  8. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
  9. Ross, Stephen A, 1981. "Some Stronger Measures of Risk Aversion in the Small and the Large with Applications," Econometrica, Econometric Society, vol. 49(3), pages 621-638, May.
  10. 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.
  11. David E. Bell & Peter C. Fishburn, 2001. "Strong One-Switch Utility," Management Science, INFORMS, vol. 47(4), pages 601-604, April.
  12. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  13. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
  14. Jean, William H, 1980. " The Geometric Mean and Stochastic Dominance," Journal of Finance, American Finance Association, vol. 35(1), pages 151-158, March.
  15. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
  16. 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.
  17. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
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