Subjective risk and disappointment
If an investor does care for utilities -and not for monetary outcomes- stochastic dominances should be expressed in terms of utility units ("utils"). If so, any "rational" investor may be characterized by an elementary utility function -called canonical utility function- which is such that the partial weak order induced by stochastic dominance over utils is as "close" to the weak order of preferences as possible. As a consequence, the random utilities of the available prospects do not violate the second-order stochastic dominance property. Substituting utils for monetary units leads to substitute "subjective" risk for "objective" risk à la Rothschild and Stiglitz (1970). A weakened independence axiom may them be set over comparable prospects, i.e. those which exhibit the same canonical expected utility. This leads to a fully choice-based theory of disappointment. The functional is lottery-dependent (Becker and Sarin 1987). When constant marginal utility is assumed, it is but the opposite to a convex measure of risk (Föllmer and Schied 2002). It may be viewed as a theoretical justification for choosing this measure of risk.
|Date of creation:||Dec 2012|
|Publication status:||Published in Documents de travail du Centre d'Economie de la Sorbonne 2012.63 - ISSN : 1955-611X - Version ré.. 2012|
|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00747902v3|
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References listed on IDEAS
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- Joao L. Becker & Rakesh K. Sarin, 1987. "Lottery Dependent Utility," Management Science, INFORMS, vol. 33(11), pages 1367-1382, November.
- Jia, Jianmin & Dyer, James S & Butler, John C, 2001. "Generalized Disappointment Models," Journal of Risk and Uncertainty, Springer, vol. 22(1), pages 59-78, January.
- Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
- Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
- Grant, Simon & Kajii, Atsushi, 1998.
"AUSI expected utility: An anticipated utility theory of relative disappointment aversion,"
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Elsevier, vol. 37(3), pages 277-290, November.
- GRANT, Simon & KAJII, Atsushi, 1994. "Ausi Expected Utility : An Anticipated Utility Theory of Relative Disappointment Aversion," CORE Discussion Papers 1994045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Jianmin Jia & James S. Dyer, 1996. "A Standard Measure of Risk and Risk-Value Models," Management Science, INFORMS, vol. 42(12), pages 1691-1705, December.
- Philippe Delquié & Alessandra Cillo, 2006. "Disappointment without prior expectation: a unifying perspective on decision under risk," Journal of Risk and Uncertainty, Springer, vol. 33(3), pages 197-215, December.
- 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.
- Graham Loomes & Robert Sugden, 1986. "Disappointment and Dynamic Consistency in Choice under Uncertainty," Review of Economic Studies, Oxford University Press, vol. 53(2), pages 271-282.
- van Dijk, Wilco W. & Zeelenberg, Marcel & van der Pligt, Joop, 2003. "Blessed are those who expect nothing: Lowering expectations as a way of avoiding disappointment," Journal of Economic Psychology, Elsevier, vol. 24(4), pages 505-516, August. Full references (including those not matched with items on IDEAS)
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