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Samuelson's Fallacy of Large Numbers With Decreasing Absolute Risk Aversion

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  • Whelan, Karl

Abstract

Samuelson (1963) conjectured that accepting multiple independent gambles you would reject on a stand-alone basis violated expected utility theory. Ross (1999) and others presented examples where expected utility maximizers would accept multiple gambles that would be rejected on a stand-alone basis once the number of gambles gets large enough. We show that a stronger result than Samuelson's conjecture applies for DARA preferences over wealth. Expected utility maximizers with DARA preferences have threshold levels of wealth such that those above the threshold will accept N positive expected value gambles while those below will not and these thresholds are increasing with N.

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  • Whelan, Karl, 2024. "Samuelson's Fallacy of Large Numbers With Decreasing Absolute Risk Aversion," CEPR Discussion Papers 19319, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:19319
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    References listed on IDEAS

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    1. Christian Gollier, 1996. "Repeated Optional Gambles and Risk Aversion," Management Science, INFORMS, vol. 42(11), pages 1524-1530, November.
    2. Dybvig, Philip H & Lippman, Steven A, 1983. "An Alternative Characterization of Decreasing Absolute Risk Aversion," Econometrica, Econometric Society, vol. 51(1), pages 223-224, January.
    3. Levy, Haim, 1994. "Absolute and Relative Risk Aversion: An Experimental Study," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 289-307, May.
    4. Ross, Stephen A., 1999. "Adding Risks: Samuelson's Fallacy of Large Numbers Revisited," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(3), pages 323-339, September.
    5. Pierre‐André Chiappori & Monica Paiella, 2011. "Relative Risk Aversion Is Constant: Evidence From Panel Data," Journal of the European Economic Association, European Economic Association, vol. 9(6), pages 1021-1052, December.
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    More about this item

    Keywords

    Risk aversion;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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