×

zbMATH — the first resource for mathematics

A possibilistic approach to risk aversion. (English) Zbl 1243.91026
Summary: In this paper a possibilistic model of risk aversion based on the lower and upper possibilistic expected values of a fuzzy number is studied. Three notions of possibilistic risk premium are defined for which calculation formulae in terms of Arrow-Pratt index and a possibilistic variance are established. A possibilistic version of Pratt theorem is proved.

MSC:
91B06 Decision theory
03E72 Theory of fuzzy sets, etc.
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Arrow KJ (1970) Essays in the theory of risk bearing, North-Holland, Amsterdam · Zbl 0215.58602
[2] Campos L, Gonzales A (1994) Further contributions to the study of average value for ranking fuzzy numbers. Int J Approx Reason 10:135–163 · Zbl 0798.90003
[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, studies in fuzziness and soft computing series, vol 82, Springer, Berlin
[5] 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
[6] Carlsson C, Fullér R, Majlender P (2005) On possibilistic correlation, Fuzzy Sets Syst 155:425–445 · Zbl 1085.94028
[7] Couso I, Dubois D, Montez S, Sanchez L (2007) On various definitions of a variance of a fuzzy random variable. In: De Cooman G, Vejnarova J, Zaffalon M (eds) International symposium of imprecise probability (ISIPTA 2007), Prague, pp 135–144
[8] Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York · Zbl 0444.94049
[9] Dubois D, Prade H (1988) Possibility theory. Plenum Press, New York · Zbl 0645.68108
[10] Dubois D, Prade H (1987) The mean value of a fuzzy number. Fuzzy Sets Syst 24:279–300 · Zbl 0634.94026
[11] Dubois D, Prade H, Fortin J (2005) The empirical variance of a set of fuzzy variable. In: Proceedings of the IEEE international conference on fuzzy systems, Reno, Nevada, 22–25 May. IEEE Press, New York, pp 885–890
[12] Fullér R, Majlender P (2003) On weighted possibilistic mean and variance of fuzzy numbers. Fuzzy Sets Syst 136:365–374 · Zbl 1022.94032
[13] Fullér R (2000) Introduction to neuro-fuzzy systems, advances in soft computing. Springer, Berlin
[14] Georgescu I (2009) Possibilistic risk aversion. Fuzzy Sets Syst 60:2608–2619 · Zbl 1186.91120
[15] Gonzales A (1990) A study of the ranking function approach through mean value. Fuzzy Sets Syst 35:29–43 · Zbl 0733.90003
[16] Laffont JJ (1993) The economics of uncertainty and information. MIT Press, Cambridge
[17] Liu B, Liu YK (2002) Expected value of fuzzy variable and fuzzy expected models. IEEE Trans Fuzzy Syst 10:445–450
[18] Liu B (2007) Uncertainty theory. Springer, Berlin · Zbl 1141.28001
[19] Majlender P (2004) A normative approach to possibility theory and decision support, PhD thesis, Turku Centre for Computer Science
[20] Pratt J (1964) Risk aversion in the small and in the large. Econometrica 32:122–130 · Zbl 0132.13906
[21] Quiggin J (1993) Generalized expected utility theory. Kluwer, Amsterdam. · Zbl 0789.90026
[22] Rothschild M, Stiglitz J (1970) Increasing risk: a definition. J Econ Theory 2:225–243
[23] 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
[24] Zhang WG, Nie ZK (2003) On possibilistic variance of fuzzy numbers. Lect Notes Comput Sci 639:398–402 · Zbl 1026.68672
[25] Zhang WG, Whang YL (2007) A comparative study of possibilistic variances and covariances of fuzzy numbers. Fundamenta Informaticae 79:257–263
[26] Zadeh LA (1965) Fuzzy sets. Inf Control 8:228–253
[27] Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28 · Zbl 0377.04002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.