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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.

Suggested Citation

  • Whelan, Karl, 2024. "Samuelson's Fallacy of Large Numbers With Decreasing Absolute Risk Aversion," MPRA Paper 121384, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:121384
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    File URL: https://mpra.ub.uni-muenchen.de/121384/1/MPRA_paper_121384.pdf
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    References listed on IDEAS

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    1. Levy, Haim, 1994. "Absolute and Relative Risk Aversion: An Experimental Study," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 289-307, May.
    2. 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.
    3. Christian Gollier, 1996. "Repeated Optional Gambles and Risk Aversion," Management Science, INFORMS, vol. 42(11), pages 1524-1530, November.
    4. 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.
    5. 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.
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    More about this item

    Keywords

    Risk aversion; Paul Samuelson; Law of large numbers;
    All these keywords.

    JEL classification:

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

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