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Expected utility operators and possibilistic risk aversion. (English) Zbl 1269.91031
Summary: In this paper expected utility operators are introduced as an abstractization of some notions of possibilistic expected utility, already existing in the literature. A general theory of possibilistic risk aversion which encompasses the already existing treatments is developed. The possibilistic risk premium associated with a fuzzy number, a utility function, an expected utility operator and a weighting function is defined. An approximate calculation formula of possibilistic risk premium expressed in terms of Arrow-Pratt index and a possibilistic variance associated with an expected utility operator is obtained. In an abstract context a Pratt-type theorem is proved.

MSC:
91B06 Decision theory
91B16 Utility theory
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[1] Arrow KJ(1970) Essays in the theory of risk bearing. North-Holland, Amsterdam · Zbl 0215.58602
[2] Aumann RJ, Serrano R (2006) An economic index of riskiness. J Political Econ 116:810–836 · Zbl 1341.91040
[3] Carlsson C, Fullér R (2001) On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets Syst 122:315–326 · Zbl 1016.94047
[4] Carlsson C, Fullér R (2002) Fuzzy reasoning in decision making and optimization. In: Studies in fuzziness and soft computing series, vol 82. Springer, Berlin · Zbl 1016.68111
[5] Carlsson C, Fullér R (2011) Possibility for decision: a possibilistic approach to real life decisions. Studies in fuzziness and soft computing series. Springer, Berlin
[6] Carlsson C, Fullér R, Majlender P (2002) A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets Syst 131:13–21 · Zbl 1027.91038
[7] Carlsson C, Fullér R, Majlender P (2005) On possibilistic correlation. Fuzzy Sets Syst 155:425–445 · Zbl 1085.94028
[8] Couso I, Dubois D, Montes S, Sanchez L (2007) On various definitions of the variance of a fuzzy random variable. In: De Couman G, Vejnarova J, Zaffalon M (eds) International symposium on imprecise probability: theories and applications (ISIPTA 2007), Prague, pp 135–144
[9] Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York · Zbl 0444.94049
[10] Dubois D, Prade H (1988) Possibility theory. Plenum, New York · Zbl 0645.68108
[11] Dubois D, Fargier H, Fortin J (2005) The empirical variance of a set of fuzzy intervals. In: Proceedings of the 2005 IEEE international conference on fuzzy systems, Reno, Nevada, 22–25 May. IEEE Press, New York, pp 885–890
[12] Eeckhoudt L, Gollier C, Schlesinger H (2005) Economic and financial decisions under risk. Princeton University Press, Princeton
[13] Fullér R (2000) Introduction to neuro-fuzzy systems. Advances in soft computing. Springer, Berlin
[14] Fullér R, Majlender P (2003) On weighted possibilistic mean and variance of fuzzy numbers. Fuzzy Sets Syst 136:365–374 · Zbl 1022.94032
[15] Georgescu I (2009) Possibilistic risk aversion. Fuzzy Sets Syst 60:2608–2619 · Zbl 1186.91120
[16] Georgescu I (2010) Possibilistic Pratt theorem. In: 8th IEEE international symposium on intelligent systems and informatics, 10–11 Sept 2010, Subotica, Serbia, pp 193–196
[17] Georgescu I (2011) A possibilistic approach to risk aversion. Soft Comput 15:795–801 · Zbl 1243.91026
[18] Hadar J, Rusell WR (1969) Rules for ordering uncertain prospects. Am Econ Rev 59:25–34
[19] Jacod J, Protter P (2000) Probability essentials. Springer, Berlin
[20] Laffont JJ (1993) The economics of uncertainty and information. MIT, Cambridge
[21] Liu B (2007) Uncertainty theory. Springer, Berlin · Zbl 1141.28001
[22] Majlender P (2004) A normative approach to possibility theory and decision support. PhD thesis, Turku Centre for Computer Science
[23] Mezei J (2011) A quantitative view of fuzzy numbers. PhD thesis, Turku Centre for Computer Science
[24] Pratt J (1964) Risk aversion in the small and in the large. Econometrica 32:122–130 · Zbl 0132.13906
[25] Quiggin J (1993) Generalized expected utility theory. Kluwer-Nijhoff, Amsterdam
[26] Rothschild M, Stiglitz J (1970) Increasing risk: a definition. J Econ Theory 2:225–243
[27] Thavaneswaran A, Appadoo SS, Pascka A (2009) Weighted possibilistic moments of fuzzy numbers with application to GARCH modeling and option pricing. Math Comput Model 49:352–368 · Zbl 1165.91414
[28] Zadeh LA (1965) Fuzzy sets. Inf Control 8:228–253
[29] Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28 · Zbl 0377.04002
[30] Zhang JP, Li SM (2005) Portfolio selection with quadratic utility function under fuzzy environment. In: Proceedings of the fourth international conference on machine learning and cybernetics, Guangzhou, 18–21 Aug 2005, pp 2529–2533
[31] Zhang WG, Nie ZK (2003) On possibilistic variance of fuzzy numbers. Lect Notes Comput Sci 2639:398–402 · Zbl 1026.68672
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