Abstract
Other than traditional decision theory, this paper employs uncertainty theory to handle indeterminacy. Uncertain variables are used to represent uncertain choices. Uncertain expected utility function is defined as an increasing function of uncertain choices. Several mathematical properties of the uncertain expected utility functions are derived using inverse uncertainty distributions. In order to compare two different choices, the first order dominance and second order dominance via uncertain expected utility functions are introduced. We also investigate risk aversion attitude and risk premium. Finally, the relationship between risk premium and risk averse attitude is investigated.
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References
Al Najjar, N., & Weinstein, J. (2009). The ambiguity aversion literature: a critical assessment. Economics and Philosophy, 25, 249–284.
Arrow, K. (1959). Rational choice functions and orderings. Econometrica, 26, 121–127.
Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management Science, 17, 141–164.
Chen, X. (2011). American option pricing formula for uncertain financial market. International Journal of Operations Research, 8(2), 32–37.
Chen, X., & Ralescu, D. A. (2012). B-spline method of uncertain statistics with application to estimating travel distance. Journal of Uncertain Systems, 6(4), 256–262.
Chen X. (2014). Uncertain calculus and uncertain finance, http://orsc.edu.cn/xwchen/ucf
Chen, X., & Gao, J. (2013). Uncertain term structure model of interest rate. Soft Computing, 17(4), 597–604.
Ellsberg, D. (1961). Risk, ambiguity, and the savage axioms. Quarterly Journal of Economics, 75, 643–669.
Epstein, L., & Schneider, M. (2008). Ambiguity, information quality and asset pricing. Journal of Finance, 63, 197–228.
Gilboa, I., & Schmeidler, D. (1989). Maxmin expected utility with non-unique prior. Journal of Mathematical Economics, 18, 141–153.
Li, S., & Peng, J. (2012). A new approach to risk comparison via uncertain measure. Industrial Engineering and Management Systems, 11(2), 176–182.
Li, S., Peng, J., & Zhang, B. (2013). The uncertain premium principle based on the distortion function. Insurance: Mathematics and Economics, 53, 317–324.
Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer-Verlag.
Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems, 2(1), 3–16.
Liu, B. (2009). Theory and practice of uncertain programming (2nd ed.). Berlin: Springer-Verlag.
Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.
Liu, B. (2010). Uncertain risk analysis and uncertain reliability analysis. Journal of Uncertain Systems, 4, 163–170.
Liu, B. (2010). Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty. Berlin: Springer-Verlag.
Liu, B. (2014). Uncertain random graph and uncertain random network. Journal of Uncertain Systems, 8(1), 3–12.
Liu, Y., & Ha, M. (2010). Expected value of function of uncertain variables. Journal of Uncertain Systems, 4, 181–186.
Liu, Y. (2013). Uncertain random programming with applications. Fuzzy Optimization and Decision Making, 12(2), 153–169.
Liu Y., Chen X., & Ralescu D. (2014). Uncertain currency model and currency option pricing. International Journal of Intelligent Systems (to be published).
Peng, J. (2013). Risk metrics of loss function for uncertain system. Fuzzy Optimization and Decision Making, 12(1), 53–64.
Peng, Z., & Chen, X. (2014). Uncertain systems are universal approximators. Journal of Uncertainty Analysis and Applications, 2, 13.
Rabin, M. (2000). Risk aversion and expected-utility theory: a calibration theorem. Econometrica, 68, 1281–1292.
Schoemaker, J. H. (1982). The expected utility model: its variants, purposes, evidence and limitations. Journal of Economic Literature, 20, 529–563.
Sheng, Y., & Gao, J. (2014). Chance distribution of the maximum flow of uncertain random network. Journal of Uncertainty Analysis and Applications, 2, 15.
Sheng, Y., & Yao, K. (2014). Some formulas of variance of uncertain random variable. Journal of Uncertainty Analysis and Applications, 2, 12.
Von-Neumann, J., & Morgenstern, O. (1953). Theory of games and economic behavior (3rd ed.). Princeton: Princeton University Press.
Wang, X. S., & Peng, Z. X. (2014). Method of moments for estimating uncertainty distributions. Journal of Uncertainty Analysis and Applications, 2, 5.
Yang, X., & Gao, J. (2013). Uncertain differential games with application to capitalism. Journal of Uncertainty Analysis and Applications, 1, 17.
Yao, K., & Ji, X. (2014). Uncertain decision making and its application to portfolio selection problem. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 22(1), 113–123.
Zhang, X., & Chen, X. (2012). A new uncertain programming model for project scheduling problem. Information: An International Interdisciplinary Journal, 15(10), 3901–3910.
Zhou J., Zhang X., Gu X. & Wang D. (2014). Uncertain risk aversion, http://orsc.edu.cn/online/140806.
Zhu, Y. (2010). Uncertain optimal control with application to a portfolio selection model. Cybernetics and Systems, 41, 535–547.
Zuo Y. & Ji X. (2009). Theoretical foundation of uncertain dominance. In proceedings of the eighth international conference on information and management sciences, Kunming, China, July 20–28, pp. 827–832.
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This work was supported by National Natural Science Foundation of China No. 61304182 and supported by “the Fundamental Research Funds for the Central Universities” No. NKZXB1419.
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Chen, X., Park, GK. Uncertain expected utility function and its risk premium. J Intell Manuf 28, 581–587 (2017). https://doi.org/10.1007/s10845-014-1007-3
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DOI: https://doi.org/10.1007/s10845-014-1007-3