IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/121384.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/121384/1/MPRA_paper_121384.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sergio Sousa, 2010. "Small-scale changes in wealth and attitudes toward risk," Discussion Papers 2010-11, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    2. Aloysius, John A., 2003. "Rational escalation of costs by playing a sequence of unfavorable gambles: the martingale," Journal of Economic Behavior & Organization, Elsevier, vol. 51(1), pages 111-129, May.
    3. Tamás Csermely & Alexander Rabas, 2016. "How to reveal people’s preferences: Comparing time consistency and predictive power of multiple price list risk elicitation methods," Journal of Risk and Uncertainty, Springer, vol. 53(2), pages 107-136, December.
    4. Moshe Levy & Adi Rizansky, 2014. "Market failure in the pharmaceutical industry and how it can be overcome: the CureShare mechanism," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 15(2), pages 143-156, March.
    5. Pfuderer, Simone, 2015. "An Experimental Approach to Testing the Competitive Storage Model," 89th Annual Conference, April 13-15, 2015, Warwick University, Coventry, UK 204297, Agricultural Economics Society.
    6. Blaufus, Kay & Hundsdoerfer, Jochen & Jacob, Martin & Sünwoldt, Matthias, 2016. "Does legality matter? The case of tax avoidance and evasion," Journal of Economic Behavior & Organization, Elsevier, vol. 127(C), pages 182-206.
    7. George Samartzis & Nikitas Pittis, 2022. "Dynamic Estimates Of The Arrow-Pratt Absolute And Relative Risk Aversion Coefficients," Papers 2211.03604, arXiv.org.
    8. Owen Freestone & Robert Breunig, 2020. "Risk Aversion and the Elasticity of Intertemporal Substitution among Australian Households," The Economic Record, The Economic Society of Australia, vol. 96(313), pages 121-139, June.
    9. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again," Econometrica, Econometric Society, vol. 89(1), pages 475-506, January.
    10. Iñigo Iturbe-Ormaetxe Kortajarene & Giovanni Ponti & Josefa Tomás Lucas, 2015. "Some (Mis)facts about Myopic Loss Aversion," Working Papers. Serie AD 2015-09, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    11. Oded Stark, 2019. "On Social Preferences and the Intensity of Risk Aversion," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 86(3), pages 807-826, September.
    12. Pierre Chaigneau & Louis Eeckhoudt, 2020. "Downside risk-neutral probabilities," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 65-77, April.
    13. Jakusch, Sven Thorsten, 2017. "On the applicability of maximum likelihood methods: From experimental to financial data," SAFE Working Paper Series 148, Leibniz Institute for Financial Research SAFE, revised 2017.
    14. Aloysius, John A., 2005. "Ambiguity aversion and the equity premium puzzle: A re-examination of experimental data on repeated gambles," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 34(5), pages 635-655, October.
    15. Sergio Sousa, 2010. "Small-scale changes in wealth and attitudes toward risk," Discussion Papers 2010-11, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    16. Tobias Huber & Johannes G. Jaspersen & Andreas Richter & Dennis Strümpel, 2023. "On the change of risk aversion in wealth: a field experiment in a closed economic system," Experimental Economics, Springer;Economic Science Association, vol. 26(1), pages 1-26, March.
    17. Levy, Moshe, 2019. "Stocks for the log-run and constant relative risk aversion preferences," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1163-1168.
    18. Kenneth Arrow & Marcel Priebsch, 2014. "Bliss, Catastrophe, and Rational Policy," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 58(4), pages 491-509, August.
    19. Francisco Martínez-Mora & M. Socorro Puy, 2009. "Off-the-peak preferences over government size," Working Papers 2009-9, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
    20. Lin William Cong & Zhiguo He & Jiasun Li & Wei Jiang, 2021. "Decentralized Mining in Centralized Pools [Concentrating on the fall of the labor share]," The Review of Financial Studies, Society for Financial Studies, vol. 34(3), pages 1191-1235.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:121384. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.