# Piecewise linear rank-dependent utility

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## 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

- Abdellaoui, M. (2002). A genuine rank-dependent generalization of the von Neumann–Morgenstern expected utility theorem.
*Econometrica*,*70*(2), 717–736.CrossRefGoogle Scholar - 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 - 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 - 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 - 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 - Cohen, M. (1992). Security level, potential level, expected utility: A three-criteria decision model under risk.
*Theory and Decision*,*24*, 101–134.CrossRefGoogle Scholar - Diecidue, E., Schmidt, U., & Zank, H. (2009). Parametric weighting functions.
*Journal of Economic Theory*,*144*(3), 1102–1118.CrossRefGoogle Scholar - Dominiak, A., & Lefort, J.-P. (2013). Agreement theorem for neo-additive beliefs.
*Economic Theory*,*52*, 1–13.Google Scholar - Dominiak, A., Eichberger, J., & Lefort, J.-P. (2012). Agreeable trade with pessimism and optimism.
*Mathematical Social Sciences*,*46*, 119–126.Google Scholar - Eichberger, J., & Kelsey, D. (2011). Are the treasures of game theory ambiguous?
*Economic Theory*,*48*, 313–339.CrossRefGoogle Scholar - Eichberger, J., & Kelsey, D. (2014). Optimism and pessimism in games.
*International Economic Review*,*55*, 483–505.CrossRefGoogle Scholar - 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 - Ford, J., Kelsey, D., & Pang, W. (2013). Ambiguity in financial markets: herding and contrarian behaviour.
*Theory and Decision*, 75, 1–15.Google Scholar - 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 - Lopes, L. L. (1987). Between hope and fear: The psychology of risk.
*Advances in Experimental Psychology*,*20*, 255–295.CrossRefGoogle Scholar - 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 - 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 - Quiggin, J. (1982). A theory of anticipated utility.
*Journal of Economic Behavior & Organization*,*3*, 323–343.CrossRefGoogle Scholar - Romm, A. T. (2014). An interpretation of focal point responses as non-additive beliefs.
*Judgment and Decision Making*,*9*(5), 387–402.Google Scholar - Teitelbaum, J. C. (2007). A unilateral accident model under ambiguity.
*The Journal of Legal Studies*,*36*, 431–477.CrossRefGoogle Scholar - Wakker, P. P. (1993). Additive representations on rank-ordered sets II: The topological approach.
*Journal of Mathematical Economics*,*22*, 1–26.CrossRefGoogle Scholar - Wakker, P. P. (1994). Separating marginal utility and probabilistic risk aversion.
*Theory and Decision*,*36*, 1–44.CrossRefGoogle Scholar - Webb, C. S. (2015). Piecewise additivity for non-expected utility.
*Economic Theory*, 60(2), 371–392.Google Scholar - Webb, C. S., & Zank, H. (2011). Accounting for optimism and pessimism in expected utility.
*Journal of Mathematical Economics*,*47*(6), 706–717.CrossRefGoogle Scholar - Wu, G., & Gonzalez, R. (1996). Curvature of the probability weighting function.
*Management Science*,*42*, 1676–1690.CrossRefGoogle Scholar - 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

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