IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v175y2018icp730-765.html
   My bibliography  Save this article

Risk sharing in the small and in the large

Author

Listed:
  • Ghirardato, Paolo
  • Siniscalchi, Marciano

Abstract

This paper analyzes risk sharing in economies with no aggregate uncertainty when agents have non-convex preferences. In particular, agents need not be globally risk-averse, or uncertainty-averse in the sense of Schmeidler (1989). We identify a behavioral condition under which betting is inefficient (i.e., every Pareto-efficient allocation provides full insurance, and conversely) if and only if agents' supporting probabilities (defined as in Rigotti et al., 2008) have a non-empty intersection. Our condition is consistent with empirical and experimental evidence documenting violations of convexity in either outcomes or utilities. Our results show that the connection between speculative betting and inconsistent beliefs does not depend upon global notions of risk or ambiguity aversion.

Suggested Citation

  • Ghirardato, Paolo & Siniscalchi, Marciano, 2018. "Risk sharing in the small and in the large," Journal of Economic Theory, Elsevier, vol. 175(C), pages 730-765.
  • Handle: RePEc:eee:jetheo:v:175:y:2018:i:c:p:730-765
    DOI: 10.1016/j.jet.2018.03.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S002205311830084X
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Irma Machielse & Danielle Timmermans & Peter Wakker, 2007. "The effects of statistical information on risk ambiguity attitudes, and on rational insurance decisions," Natural Field Experiments 00338, The Field Experiments Website.
    2. Olivier L’Haridon & Lætitia Placido, 2010. "Betting on Machina’s reflection example: an experiment on ambiguity," Theory and Decision, Springer, vol. 69(3), pages 375-393, September.
    3. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    4. Paolo Ghirardato & Marciano Siniscalchi, 2012. "Ambiguity in the Small and in the Large," Econometrica, Econometric Society, vol. 80(6), pages 2827-2847, November.
    5. Aurelien Baillon & Olivier L'Haridon & Laetitia Placido, 2011. "Ambiguity Models and the Machina Paradoxes," American Economic Review, American Economic Association, vol. 101(4), pages 1547-1560, June.
    6. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    7. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Valuation equilibrium and pareto optimum in non-convex economies," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 293-308, April.
    8. Aloisio Araujo & Jean-Marc Bonnisseau & Alain Chateauneuf & Rodrigo Novinski, 2014. "Optimal Risk Sharing with Optimistic and Pessimistic Decision Makers," Working Papers 2014-579, Department of Research, Ipag Business School.
    9. Mark J. Machina, 2009. "Risk, Ambiguity, and the Rank-Dependence Axioms," American Economic Review, American Economic Association, vol. 99(1), pages 385-392, March.
    10. Dekel, Eddie, 1989. "Asset Demands without the Independence Axiom," Econometrica, Econometric Society, vol. 57(1), pages 163-169, January.
    11. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    12. Kajii, Atsushi & Ui, Takashi, 2006. "Agreeable bets with multiple priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 299-305, May.
    13. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallou, 2002. "Sharing beliefs and the absence of betting in the Choquet expected utility model," Statistical Papers, Springer, vol. 43(1), pages 127-136, January.
    14. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing Beliefs: Between Agreeing and Disagreeing," Econometrica, Econometric Society, vol. 68(3), pages 685-694, May.
    15. Dominiak, Adam & Eichberger, Jürgen & Lefort, Jean-Philippe, 2012. "Agreeable trade with optimism and pessimism," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 119-126.
    16. Chevalier, Judith & Ellison, Glenn, 1997. "Risk Taking by Mutual Funds as a Response to Incentives," Journal of Political Economy, University of Chicago Press, vol. 105(6), pages 1167-1200, December.
    17. Peter P. Wakker & Daniëlle R. M. Timmermans & Irma Machielse, 2007. "The Effects of Statistical Information on Risk and Ambiguity Attitudes, and on Rational Insurance Decisions," Management Science, INFORMS, vol. 53(11), pages 1770-1784, November.
    18. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    19. Strzalecki, Tomasz & Werner, Jan, 2011. "Efficient allocations under ambiguity," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1173-1194, May.
    20. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
    21. Brown, Donald J., 1991. "Equilibrium analysis with non-convex technologies," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.),Handbook of Mathematical Economics, edition 1, volume 4, chapter 36, pages 1963-1995, Elsevier.
    22. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    23. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    24. Marciano Siniscalchi, 2009. "Vector Expected Utility and Attitudes Toward Variation," Econometrica, Econometric Society, vol. 77(3), pages 801-855, May.
    25. Alok Kumar, 2009. "Who Gambles in the Stock Market?," Journal of Finance, American Finance Association, vol. 64(4), pages 1889-1933, August.
    26. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    27. Curley, Shawn P. & Yates, J. Frank, 1985. "The center and range of the probability interval as factors affecting ambiguity preferences," Organizational Behavior and Human Decision Processes, Elsevier, vol. 36(2), pages 273-287, October.
    28. Heath, Chip & Tversky, Amos, 1991. "Preference and Belief: Ambiguity and Competence in Choice under Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 5-28, January.
    29. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    30. Adam Dominiak & Jürgen Eichberger & Jean-Philippe Lefort, 2012. "Agreeable trade with pessimism and optimism," Post-Print hal-01615843, HAL.
    31. repec:dau:papers:123456789/5461 is not listed on IDEAS
    32. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    33. repec:dau:papers:123456789/8588 is not listed on IDEAS
    34. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 579-608.
    35. Luca Rigotti & Chris Shannon & Tomasz Strzalecki, 2008. "Subjective Beliefs and ex ante Trade," Econometrica, Econometric Society, vol. 76(5), pages 1167-1190, September.
    36. J.-P. Penot & P. H. Quang, 1997. "Generalized Convexity of Functions and Generalized Monotonicity of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 343-356, February.
    37. Araujo A. & Chateauneuf A. & Gama-Torres J. & Novinski R., 2014. "General equilibrium, risk taking and volatility," Working Papers 2014-181, Department of Research, Ipag Business School.
    38. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, Oxford University Press, vol. 75(4), pages 643-669.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Antoine Billot & Sujoy Mukerji & Jean-Marc Tallon, 2020. "Market Allocations under Ambiguity: A Survey," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 267-282.
    2. Galanis, S., 2019. "Dynamic Consistency, Valuable Information and Subjective Beliefs," Working Papers 19/02, Department of Economics, City University London.
    3. Galanis, Spyros, 2018. "Financial complexity and trade," Games and Economic Behavior, Elsevier, vol. 112(C), pages 219-230.

    More about this item

    Keywords

    Risk sharing; Pareto efficiency; Ambiguity aversion; Non-convex preferences;

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D60 - Microeconomics - - Welfare Economics - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:eee:jetheo:v:175:y:2018:i:c:p:730-765. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Haili He). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.