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Choice under risk and the security factor: an axiomatic model. (English) Zbl 0631.90005
The particular attention paid by decision makers to the security level ensured by each decision under risk, which is responsible for the certainty effect, can be taken into account by weakening the independence and continuity axioms of expected utility theory. In the resulting model, preferences depend on: (i) the security level, (ii) the expected utility, offered by each decision. Choices are partially determined by security level comparison and completed by the maximization of a function, which express the existing tradeoffs between expected utility and security level, and is, at a given security level, an affine function of the expected utility. In the model, risk neutrality at a given security level implies risk aversion.

##### MSC:
 91B16 Utility theory 91B06 Decision theory
##### Keywords:
risk aversion; security level; expected utility; risk neutrality
Full Text:
##### References:
 [1] Allais, M.: 1952, ?The foundations of a positive theory of choice involving risk and a criticism of the postulate and axioms of the American School? (From 1952, French version). In M. Allais and Hagen (Eds): 1979, Expected Utility Hypotheses and the Allais Paradox, D. Reidel, Dordrecht, 27-145. [2] Chew, S. H.: 1981, ?A Mixture Set Axiomatization of Weighted Utility Theory?, Unpublished Manuscript, U. of Arizona. [3] Ferguson, T. S.: 1967, Mathematical Statistics, Academic Press, New York. · Zbl 0153.47602 [4] Fishburn, P. C.: 1982, The Foundations of Expected Utility, D. Reidel, Dordrecht. · Zbl 0497.90001 [5] Gilboa, I.: 1986, ?A combination of Expected Utility and Maxmin Decision Criteria?, Tel Aviv University, Working Paper # 12-86. [6] Hammond, P. J.: 1976, ?Changing Tastes and Coherent Dynamic Choice? Review of Economic Studies 43, 159-174. · Zbl 0367.90011 [7] Hershey, J. C., Kunreuther, H. C., and Schoemaker, P. J. H.: ?Sources of Bias in Assessment Procedures for Utility Functions?, Management Sci. 28, 936-954. · Zbl 0487.90013 [8] Kahneman, D. and Tversky, A.: 1979, ?Prospect Theory: An Analysis of Decision under Risk?, Econometrica 47, 263-291. · Zbl 0411.90012 [9] Lopes, L. L.: 1986, ?Between Hope and Fear: The Psychology of Risk?, Advances in Experimental Social Psychology (in press). [10] Machina, M. J.: 1982, ??Expected Utility? Analysis without the Independence Axiom?, Econometrica 50, 277-323. · Zbl 0475.90015 [11] McCord, M. R. and de Neufville, R.: 1986, ??Lottery equivalents?: Reduction of the certainty effect problem in utility assessment?, Management Sci. 32, 56-60. · Zbl 0599.90008 [12] Quiggin, J.: 1982, ?A Theory of Anticipated Utility?, Journal of Economic Behavior and Organization 3, 323-343. [13] Segal, U.: 1984, ?Non linear Decision Weights with the Independence Axiom?, UCLA Working Paper # 353. [14] von Neumann, J. and Morgenstern, O.: 1944, Theory of Games and Economic Behavior, Princeton University Press, Princeton. · Zbl 0063.05930 [15] Yaari, M. E.: 1987, ?The Dual Theory of Choice Under Risk?, Econometrica 55, 95-115. · Zbl 0616.90005
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