A possibilistic approach to risk aversion Original Paper

First Online: 10 July 2010 DOI :
10.1007/s00500-010-0634-7

Cite this article as: Georgescu, I. Soft Comput (2010) 15: 795. doi:10.1007/s00500-010-0634-7 Abstract 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.

Keywords Possibilistic indicators Possibilistic risk premium Possibilistic Pratt theorem

References Arrow KJ (1970) Essays in the theory of risk bearing, North-Holland, Amsterdam

MATH Campos L, Gonzales A (1994) Further contributions to the study of average value for ranking fuzzy numbers. Int J Approx Reason 10:135–163

MATH CrossRef Carlsson C, Fullér R (2001) On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets Syst 122:315–326

MATH CrossRef Carlsson C, Fullér R (2002) Fuzzy reasoning in decision making and optimization, studies in fuzziness and soft computing series, vol 82, Springer, Berlin

Carlsson C, Fullér R, Majlender P (2002) A possibilistic approach to selecting portfolios with highest utility score, Fuzzy Sets Syst 131:13–21

MATH CrossRef Carlsson C, Fullér R, Majlender P (2005) On possibilistic correlation, Fuzzy Sets Syst 155:425–445

MATH CrossRef 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

Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York

MATH Dubois D, Prade H (1988) Possibility theory. Plenum Press, New York

MATH Dubois D, Prade H (1987) The mean value of a fuzzy number. Fuzzy Sets Syst 24:279–300

MathSciNet MATH CrossRef 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

Fullér R, Majlender P (2003) On weighted possibilistic mean and variance of fuzzy numbers. Fuzzy Sets Syst 136:365–374

Fullér R (2000) Introduction to neuro-fuzzy systems, advances in soft computing. Springer, Berlin

Georgescu I (2009) Possibilistic risk aversion. Fuzzy Sets Syst 60:2608–2619

MathSciNet CrossRef Gonzales A (1990) A study of the ranking function approach through mean value. Fuzzy Sets Syst 35:29–43

CrossRef Laffont JJ (1993) The economics of uncertainty and information. MIT Press, Cambridge

Liu B, Liu YK (2002) Expected value of fuzzy variable and fuzzy expected models. IEEE Trans Fuzzy Syst 10:445–450

CrossRef Liu B (2007) Uncertainty theory. Springer, Berlin

MATH Majlender P (2004) A normative approach to possibility theory and decision support, PhD thesis, Turku Centre for Computer Science

Pratt J (1964) Risk aversion in the small and in the large. Econometrica 32:122–130

MATH CrossRef Quiggin J (1993) Generalized expected utility theory. Kluwer, Amsterdam.

Rothschild M, Stiglitz J (1970) Increasing risk: a definition. J Econ Theory 2:225–243

MathSciNet CrossRef 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

MATH CrossRef Zhang WG, Nie ZK (2003) On possibilistic variance of fuzzy numbers. Lect Notes Comput Sci 639:398–402

CrossRef Zhang WG, Whang YL (2007) A comparative study of possibilistic variances and covariances of fuzzy numbers. Fundamenta Informaticae 79:257–263

MathSciNet MATH Zadeh LA (1965) Fuzzy sets. Inf Control 8:228–253

MathSciNet CrossRef Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28

MathSciNet MATH CrossRef Authors and Affiliations 1. Department of Economic Cybernetics Academy of Economic Studies Bucharest Romania