Abstract
This paper concerns SSB utility theory in the monetary context. It introduces a measure of risk aversion and establishes necessary and sufficient conditions for comparative risk aversion. Nonseparable decompositions of an SSB utility function that have the form Φ(x, y)=w(x)w(y)f(x−y) are examined. Risk properties such as constant risk aversion and a delta property are shown to give specific functional forms for an SSB utility function.
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References
J. Aczel,Lectures on Functional Equations and Their Applications (Academic Press, New York, 1966).
K.J. Arrow,Essays in the Theory of Risk-bearing (Markham, Chicago, Illinois, 1971).
J.L. Becker and R.K. Sarin, Lottery dependent utility, Manag. Sci. 33(1987)1367.
D.E. Bell, Regret in decision making under uncertainty, Oper. Res. 30(1982)961.
D.E. Bell and P.H. Farquhar, Perspectives on utility theory, Oper. Res. 34(1986)179.
S.H. Chew, A mixture set axiomatization of weighted utility theory, Working Paper, University of Arizona (1982).
S.H. Chew, A generalization of the quasilinear mean with applications to the measurement of income inequality and decision theory resolving the Allais paradox, Econometrica 51(1983)1065.
S.H. Chew and K.R. MacCrimmon, Alpha-nu choice theory: A generalization of expected utility theory, Working Paper No. 669, University of British Columbia (1979).
P.C. Fishburn, Nontransitive measurable utility, J. Mathematical Psychology 26(1982)31.
P.C. Fishburn, Transitive measurable utility, J. Economic Theory 31(1983)293.
P.C. Fishburn, Elements of risk analysis in nonlinear utility theory, INFOR 22(1984)81.
P.C. Fishburn, SSB utility theory: An economic perspective, Mathematical Social Sciences 8(1984)63.
P.C. Fishburn, Implicit mean value and certainty equivalence, Econometrica 54(1986)1197.
D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica 47(1979)263.
U.S. Karmarkar, Subjectively weighted utility: A descriptive extension of the expected utility model, Organizational Behavior and Human Performance 21(1978)61.
R.L. Keeney and H. Raiffa,Decisions with Multiple Objectives: Preferences and Value Tradeoffs (Wiley, New York, 1976).
G. Loomes and R. Sugden, Regret theory: An alternative theory of rational choice under uncertainty, The Economic Journal 92(1982)805.
M.J. Machina, “Expected utility” analysis without the independence axiom, Econometrica 50(1982)277.
M.J. Machina, A stronger characterization of declining risk aversion, Econometrica 50(1982)1069.
Y. Nakamura, Nonlinear measurable utility analysis, Ph.D. Thesis, University of California, Davis (1984).
J.W. Pratt, Risk aversion in the small and in the large, Econometrica 32(1964)122.
J. Quiggin, Anticipated utility theory, J. Economic Behavior and Organization 3(1982)323.
S.A. Ross, Some stronger measure of risk aversion in the small and the large with applications, Econometrica 49(1981)621.
J. von Neumann and O. Morgenstern,Theory of Games and Economic Behavior, 2nd ed. (Princeton University Press, New Jersey, 1947).
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Nakamura, Y. Risk attitudes for nonlinear measurable utility. Ann Oper Res 19, 311–333 (1989). https://doi.org/10.1007/BF02283527
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DOI: https://doi.org/10.1007/BF02283527