Soft Computing

, Volume 15, Issue 4, pp 795–801 | Cite as

A possibilistic approach to risk aversion

Original Paper


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.


Possibilistic indicators Possibilistic risk premium Possibilistic Pratt theorem 


  1. Arrow KJ (1970) Essays in the theory of risk bearing, North-Holland, AmsterdamMATHGoogle Scholar
  2. Campos L, Gonzales A (1994) Further contributions to the study of average value for ranking fuzzy numbers. Int J Approx Reason 10:135–163MATHCrossRefGoogle Scholar
  3. Carlsson C, Fullér R (2001) On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets Syst 122:315–326MATHCrossRefGoogle Scholar
  4. Carlsson C, Fullér R (2002) Fuzzy reasoning in decision making and optimization, studies in fuzziness and soft computing series, vol 82, Springer, BerlinGoogle Scholar
  5. Carlsson C, Fullér R, Majlender P (2002) A possibilistic approach to selecting portfolios with highest utility score, Fuzzy Sets Syst 131:13–21MATHCrossRefGoogle Scholar
  6. Carlsson C, Fullér R, Majlender P (2005) On possibilistic correlation, Fuzzy Sets Syst 155:425–445MATHCrossRefGoogle Scholar
  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 135–144Google Scholar
  8. Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New YorkMATHGoogle Scholar
  9. Dubois D, Prade H (1988) Possibility theory. Plenum Press, New YorkMATHGoogle Scholar
  10. Dubois D, Prade H (1987) The mean value of a fuzzy number. Fuzzy Sets Syst 24:279–300MathSciNetMATHCrossRefGoogle Scholar
  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 885–890Google Scholar
  12. Fullér R, Majlender P (2003) On weighted possibilistic mean and variance of fuzzy numbers. Fuzzy Sets Syst 136:365–374Google Scholar
  13. Fullér R (2000) Introduction to neuro-fuzzy systems, advances in soft computing. Springer, BerlinGoogle Scholar
  14. Georgescu I (2009) Possibilistic risk aversion. Fuzzy Sets Syst 60:2608–2619MathSciNetCrossRefGoogle Scholar
  15. Gonzales A (1990) A study of the ranking function approach through mean value. Fuzzy Sets Syst 35:29–43CrossRefGoogle Scholar
  16. Laffont JJ (1993) The economics of uncertainty and information. MIT Press, CambridgeGoogle Scholar
  17. Liu B, Liu YK (2002) Expected value of fuzzy variable and fuzzy expected models. IEEE Trans Fuzzy Syst 10:445–450CrossRefGoogle Scholar
  18. Liu B (2007) Uncertainty theory. Springer, BerlinMATHGoogle Scholar
  19. Majlender P (2004) A normative approach to possibility theory and decision support, PhD thesis, Turku Centre for Computer ScienceGoogle Scholar
  20. Pratt J (1964) Risk aversion in the small and in the large. Econometrica 32:122–130MATHCrossRefGoogle Scholar
  21. Quiggin J (1993) Generalized expected utility theory. Kluwer, Amsterdam.Google Scholar
  22. Rothschild M, Stiglitz J (1970) Increasing risk: a definition. J Econ Theory 2:225–243MathSciNetCrossRefGoogle Scholar
  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: 352–368MATHCrossRefGoogle Scholar
  24. Zhang WG, Nie ZK (2003) On possibilistic variance of fuzzy numbers. Lect Notes Comput Sci 639:398–402CrossRefGoogle Scholar
  25. Zhang WG, Whang YL (2007) A comparative study of possibilistic variances and covariances of fuzzy numbers. Fundamenta Informaticae 79:257–263MathSciNetMATHGoogle Scholar
  26. Zadeh LA (1965) Fuzzy sets. Inf Control 8:228–253MathSciNetCrossRefGoogle Scholar
  27. Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Economic CyberneticsAcademy of Economic StudiesBucharestRomania

Personalised recommendations