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 ˆ 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 (Fšllmer and Schied 2002). It may be viewed as a theoretical justification for choosing this measure of risk.
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- 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.
- 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.
- 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).
- Grant, Simon & Kajii, Atsushi, 1998. "AUSI expected utility: An anticipated utility theory of relative disappointment aversion," Journal of Economic Behavior & Organization, Elsevier, vol. 37(3), pages 277-290, November.
- Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
- 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.
- Joao L. Becker & Rakesh K. Sarin, 1987. "Lottery Dependent Utility," Management Science, INFORMS, vol. 33(11), pages 1367-1382, November.
- 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.
- 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.
- Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-86, May.
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