Abstract
In this chapter a new model of choice under risk within the framework of RDU theory is offered. The suggested model contains the expected utility model as a special case. Compared to anticipated utility theory it is more general in one respect and more restrictive in another. It is more general since it allows the probability distortion to depend on the prizes available. But it restricts on the other hand these distortions to be homogeneous in the probabilities.
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Notes
For an approach to this problem without further assumptions but with a considerable amount of technical details see the appendix of [Chew and Epstein 1989].
The assumption of absolute continuity is much weaker than the condition of differentiability on basic distributions used in [Green and Jullien 1988].
Note that v1(x, ·) is continuous for every x ∈ X since (Inp)p9(x) → 0 for p → 0, and vi(x, ·) is differentiate for p ∈ (0,1].
The class of RDU functionals which are both, multiplicatively separable and homogeneous, has been studied in [Segal 1987b] in context with the Ellsberg paradox.
This was found by many researchers (see e.g. [Preston and Baratta 1948] and the literature cited in chapter 1).
In fact, for some classes of generalized utility functions the assumption of being strictly decreasing with p would imply violations of first-order stochastic dominance. An example of such a generalized utility function is the homogeneous function (2.7).
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© 1991 Springer-Verlag Berlin Heidelberg
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Puppe, C. (1991). A Rank-Dependent Utility Model with Prize-Dependent Distortion of Probabilities. In: Distorted Probabilities and Choice under Risk. Lecture Notes in Economics and Mathematical Systems, vol 363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58203-5_3
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DOI: https://doi.org/10.1007/978-3-642-58203-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54247-6
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