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When Ross meets Bell: The linex utility function

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  • Denuit, Michel M.
  • Eeckhoudt, Louis
  • Schlesinger, Harris

Abstract

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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  • Denuit, Michel M. & Eeckhoudt, Louis & Schlesinger, Harris, 2013. "When Ross meets Bell: The linex utility function," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 177-182.
    • Handle: RePEc:eee:mateco:v:49:y:2013:i:2:p:177-182
    DOI: 10.1016/j.jmateco.2013.01.006
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    1. Dionne, Georges & Li, Jingyuan, 2014. "Comparative Ross risk aversion in the presence of mean dependent risks," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 128-135.
    2. Georges Dionne & Jingyuan Li & Cedric Okou, 2012. "An Extension of the Consumption-based CAPM Model," Cahiers de recherche 1214, CIRPEE.
    3. Carlos Rodríguez Raposo & Pablo Coello Pulido, 2021. "Ergodicity transformation for additive-ruin wealth dynamic," Working Papers hal-03198073, HAL.
    4. Louis Eeckhoudt & Liqun Liu & Jack Meyer, 2017. "Restricted increases in risk aversion and their application," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 161-181, June.
    5. Pelin G. Canbolat, 2019. "Stochastic Contests with Linex Utility Functions," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 7(1), pages 113-128, June.
    6. Georges Dionne & Jingyuan Li, 2012. "Comparative Ross Risk Aversion in the Presence of Quadrant Dependent Risks," Cahiers de recherche 1226, CIRPEE.
    7. Wang, Jianli & Li, Jingyuan, 2014. "Decreasing Ross risk aversion: Higher-order generalizations and implications," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 136-142.
    8. Liu, Liqun & Meyer, Jack, 2013. "Substituting one risk increase for another: A method for measuring risk aversion," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2706-2718.
    9. Liqun Liu & Jack Meyer, 2013. "Normalized measures of concavity and Ross’s strongly more risk averse order," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 185-198, October.

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