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Solution of a functional equation arising in an axiomatization of the utility of binary gambles
Author(s):
János
Aczél;
Gyula
Maksa;
Zsolt
Páles
Journal:
Proc. Amer. Math. Soc.
129
(2001),
483-493.
MSC (2000):
Primary 39B22, 39B72, 39B12;
Secondary 26A51, 91B16
Posted:
August 29, 2000
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Abstract:
For a new axiomatization, with fewer and weaker assumptions, of binary rank-dependent expected utility of gambles the solution of the functional equation
is needed under some monotonicity and surjectivity conditions. We furnish the general such solution and also the solutions under weaker suppositions. In the course of the solution we also determine all sign preserving solutions of the related general equation
References:
-
- 1.
- J. Aczél, Lectures on Functional Equations and their Applications, Academic Press, New York/London, 1966. MR 34:8020
- 2.
- E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer, New York/Heidelberg, 1975. MR 51:3363
- 3.
- M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Panstwowe Wydawnictwo Naukowe, Warszawa/Kraków/Katowice, 1985. MR 86i:39008
- 4.
- A. A. J. Marley and R. D. Luce, A simple axiomatization of binary rank-dependent expected utility for gains (losses), submitted.
- 5.
- F. Riesz and B. Szokefalvi-Nagy, Functional Analysis, Dover, New York, 1990. MR 91g:00002
- 6.
- A. W. Roberts and D. E. Varberg, Convex Functions, Academic Press, New York and London, 1973. MR 56:1201
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Additional Information:
János
Aczél
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Address at time of publication:
Institute for Mathematical Behavioral Sciences, SSP, University of California, Irvine, California 92697-5100
Email:
jdaczel@math.uwaterloo.ca, janos@aris.ss.uci.edu
Gyula
Maksa
Affiliation:
Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary
Email:
maksa@math.klte.hu
Zsolt
Páles
Affiliation:
Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary
Email:
pales@math.klte.hu
DOI:
10.1090/S0002-9939-00-05545-3
PII:
S 0002-9939(00)05545-3
Keywords:
Functional equation,
binary gamble,
convexity
Received by editor(s):
October 23, 1998
Received by editor(s) in revised form:
April 27, 1999
Posted:
August 29, 2000
Additional Notes:
This research has been supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada Grant OGP 002972, by the Hungarian National Research Science Foundation (OTKA) Grant T-016846 and by the Fund for Development and Research in Higher Education (FKFP) Grant 0310/1997. The authors are grateful to R. Duncan Luce (University of California, Irvine) for the problem and for advice, in particular regarding the Introduction.
Communicated by:
David R. Larson
Copyright of article:
Copyright
2000,
American Mathematical Society
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