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Comparative statics in an ordinal theory of choice under risk

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  • Chiu, W. Henry

Abstract

This paper considers the effects of changes in risk on optimal decisions under risk in an analytical framework that is capable of replicating and extending important results obtained in the EU framework and is yet far more descriptive and no less tractable at the same time. We show that a version of the general framework can be used to establish in the class of problems considered by Rothschild and Stiglitz (1971) and Machina (1989) the equivalence between behavioral assumptions and the characteristics of the utility function, which are in turn necessary and sufficient for comparative statics results.

Suggested Citation

  • Chiu, W. Henry, 2019. "Comparative statics in an ordinal theory of choice under risk," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 113-123.
  • Handle: RePEc:eee:matsoc:v:101:y:2019:i:c:p:113-123
    DOI: 10.1016/j.mathsocsci.2019.07.004
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    1. Michèle D. Cohen, 1995. "Risk-Aversion Concepts in Expected- and Non-Expected-Utility Models," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 20(1), pages 73-91, June.
    2. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    3. Menezes, Carmen F. & Wang, X.Henry, 2005. "Increasing outer risk," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 875-886, November.
    4. Dekel, Eddie, 1989. "Asset Demands without the Independence Axiom," Econometrica, Econometric Society, vol. 57(1), pages 163-169, January.
    5. Alain Chateauneuf & Ghizlane Lakhnati, 2007. "From sure to strong diversification," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 511-522, September.
    6. Eeckhoudt, Louis & Schlesinger, Harris, 2008. "Changes in risk and the demand for saving," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1329-1336, October.
    7. Cheng, Hsueh-Cheng & Magill, Michael J P & Shafer, Wayne J, 1987. "Some Results on Comparative Statics under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(2), pages 493-507, June.
    8. Wu, George, 1994. "An Empirical Test of Ordinal Independence," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 39-60, July.
    9. W. Chiu & Louis Eeckhoudt, 2010. "The effects of stochastic wages and non-labor income on labor supply: update and extensions," Journal of Economics, Springer, vol. 100(1), pages 69-83, May.
    10. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
    11. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    12. W. Chiu & Louis Eeckhoudt & Beatrice Rey, 2012. "On relative and partial risk attitudes: theory and implications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 151-167, May.
    13. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
    14. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    15. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    16. Mark J. Machina, 2014. "Ambiguity Aversion with Three or More Outcomes," American Economic Review, American Economic Association, vol. 104(12), pages 3814-3840, December.
    17. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    18. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    19. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    20. Mark J. Machina, 2009. "Risk, Ambiguity, and the Rank-Dependence Axioms," American Economic Review, American Economic Association, vol. 99(1), pages 385-392, March.
    21. Hayne E. Leland, 1968. "Saving and Uncertainty: The Precautionary Demand for Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 82(3), pages 465-473.
    22. Wang Tan, 1993. "Lp-Frechet Differentiable Preference and Local Utility Analysis," Journal of Economic Theory, Elsevier, vol. 61(1), pages 139-159, October.
    23. Hadar, Josef & Seo, Tae Kun, 1990. "The Effects of Shifts in a Return Distribution on Optimal Portfolios," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 721-736, August.
    24. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    25. Machina, Mark J., 1989. "Comparative statics and non-expected utility preferences," Journal of Economic Theory, Elsevier, vol. 47(2), pages 393-405, April.
    26. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    27. Machina, Mark J & Pratt, John W, 1997. "Increasing Risk: Some Direct Constructions," Journal of Risk and Uncertainty, Springer, vol. 14(2), pages 103-127, March.
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