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.
Similar content being viewed by others
References
Arrow KJ (1970) Essays in the theory of risk bearing, North-Holland, Amsterdam
Campos L, Gonzales A (1994) Further contributions to the study of average value for ranking fuzzy numbers. Int J Approx Reason 10:135–163
Carlsson C, Fullér R (2001) On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets Syst 122:315–326
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
Carlsson C, Fullér R, Majlender P (2005) On possibilistic correlation, Fuzzy Sets Syst 155:425–445
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
Dubois D, Prade H (1988) Possibility theory. Plenum Press, New York
Dubois D, Prade H (1987) The mean value of a fuzzy number. Fuzzy Sets Syst 24:279–300
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
Gonzales A (1990) A study of the ranking function approach through mean value. Fuzzy Sets Syst 35:29–43
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
Liu B (2007) Uncertainty theory. Springer, Berlin
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
Quiggin J (1993) Generalized expected utility theory. Kluwer, Amsterdam.
Rothschild M, Stiglitz J (1970) Increasing risk: a definition. J Econ Theory 2:225–243
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
Zhang WG, Nie ZK (2003) On possibilistic variance of fuzzy numbers. Lect Notes Comput Sci 639:398–402
Zhang WG, Whang YL (2007) A comparative study of possibilistic variances and covariances of fuzzy numbers. Fundamenta Informaticae 79:257–263
Zadeh LA (1965) Fuzzy sets. Inf Control 8:228–253
Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Georgescu, I. A possibilistic approach to risk aversion. Soft Comput 15, 795–801 (2010). https://doi.org/10.1007/s00500-010-0634-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-010-0634-7