Theory and Decision

, Volume 82, Issue 3, pp 403–414 | Cite as

Piecewise linear rank-dependent utility

Article

Abstract

Choice under risk is modelled using a piecewise linear version of rank-dependent utility. This model can be considered a continuous version of NEO-expected utility (Chateauneuf et al., J Econ Theory 137:538–567, 2007). In a framework of objective probabilities, a preference foundation is given, without requiring a rich structure on the outcome set. The key axiom is called complementary additivity.

Keywords

Rank-dependent utility Security and potential level preferences Optimism Pessimism 

JEL Classification

D81 

Notes

Acknowledgments

I am grateful for the comments of an anonymous reviewer. The usual disclaimer applies.

References

  1. Abdellaoui, M. (2002). A genuine rank-dependent generalization of the von Neumann–Morgenstern expected utility theorem. Econometrica, 70(2), 717–736.CrossRefGoogle Scholar
  2. Abdellaoui, M., & Munier, B. (1998). On the fundamental risk-structure dependence of individual preferences under risk: An experimental investigation. Annals of Operations Research, 80, 237–252.CrossRefGoogle Scholar
  3. Abdellaoui, M., L’Haridon, O., & Zank, H. (2010). Separating curvature and elevation: A parametric probability weighting function. Journal of Risk and Uncertainty, 4, 39–65.CrossRefGoogle Scholar
  4. Allais, M. (1952). The foundations of a positive theory of choice involving risk and a criticism of the postulates and axioms of the American school. In M. Allais and O. Hagen (Eds.), Expected utility and the Allais paradox. Dordrecht: D. Reidel Publishing Company.Google Scholar
  5. Chateauneuf, A., Eichberger, J., & Grant, S. (2007). Choice under uncertainty with best and worst in mind: NEO-additive capacities. Journal of Economic Theory, 137, 538–567.CrossRefGoogle Scholar
  6. Cohen, M. (1992). Security level, potential level, expected utility: A three-criteria decision model under risk. Theory and Decision, 24, 101–134.CrossRefGoogle Scholar
  7. Diecidue, E., Schmidt, U., & Zank, H. (2009). Parametric weighting functions. Journal of Economic Theory, 144(3), 1102–1118.CrossRefGoogle Scholar
  8. Dominiak, A., & Lefort, J.-P. (2013). Agreement theorem for neo-additive beliefs. Economic Theory, 52, 1–13.Google Scholar
  9. Dominiak, A., Eichberger, J., & Lefort, J.-P. (2012). Agreeable trade with pessimism and optimism. Mathematical Social Sciences, 46, 119–126.Google Scholar
  10. Eichberger, J., & Kelsey, D. (2011). Are the treasures of game theory ambiguous? Economic Theory, 48, 313–339.CrossRefGoogle Scholar
  11. Eichberger, J., & Kelsey, D. (2014). Optimism and pessimism in games. International Economic Review, 55, 483–505.CrossRefGoogle Scholar
  12. Eichberger, J., Grant, S., & Lefort, J.-P. (2012). Generalized neo-additive capacities and updating. International Journal of Economic Theory, 8(3), 237–257.CrossRefGoogle Scholar
  13. Ford, J., Kelsey, D., & Pang, W. (2013). Ambiguity in financial markets: herding and contrarian behaviour. Theory and Decision, 75, 1–15.Google Scholar
  14. Köbberling, V., & Wakker, P. P. (2003). Preference foundations for nonexpected utility: A generalized and simplified technique. Mathematics of Operations Research, 28, 395–423.CrossRefGoogle Scholar
  15. Lopes, L. L. (1987). Between hope and fear: The psychology of risk. Advances in Experimental Psychology, 20, 255–295.CrossRefGoogle Scholar
  16. Lopes, L. L. (1996). When time is of the essence: Averaging, aspiration, and the short run. Organizational Behavior and Human Decision Processes, 65, 179–189.CrossRefGoogle Scholar
  17. Ludwig, A., & Zimper, A. (2014). Biased Bayesian learning with an application to the risk-free rate puzzle. Journal of Economic Dynamics and Control, 39, 79–97.CrossRefGoogle Scholar
  18. Quiggin, J. (1982). A theory of anticipated utility. Journal of Economic Behavior & Organization, 3, 323–343.CrossRefGoogle Scholar
  19. Romm, A. T. (2014). An interpretation of focal point responses as non-additive beliefs. Judgment and Decision Making, 9(5), 387–402.Google Scholar
  20. Teitelbaum, J. C. (2007). A unilateral accident model under ambiguity. The Journal of Legal Studies, 36, 431–477.CrossRefGoogle Scholar
  21. Wakker, P. P. (1993). Additive representations on rank-ordered sets II: The topological approach. Journal of Mathematical Economics, 22, 1–26.CrossRefGoogle Scholar
  22. Wakker, P. P. (1994). Separating marginal utility and probabilistic risk aversion. Theory and Decision, 36, 1–44.CrossRefGoogle Scholar
  23. Webb, C. S. (2015). Piecewise additivity for non-expected utility. Economic Theory, 60(2), 371–392.Google Scholar
  24. Webb, C. S., & Zank, H. (2011). Accounting for optimism and pessimism in expected utility. Journal of Mathematical Economics, 47(6), 706–717.CrossRefGoogle Scholar
  25. Wu, G., & Gonzalez, R. (1996). Curvature of the probability weighting function. Management Science, 42, 1676–1690.CrossRefGoogle Scholar
  26. Zimper, A. (2012). Asset pricing in a Lucas fruit tree economy with the best and worst in mind. Journal of Economic Dynamics and Control, 36(4), 610–628.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Economics, School of Social SciencesThe University of ManchesterManchesterUK

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