Choices Under Risk

  • Emilio Barucci
  • Claudio Fontana
Chapter
Part of the Springer Finance book series (FINANCE)

Abstract

This chapter presents the foundations of decision making problems in a risky environment. By introducing suitable axioms on the preference relation, the existence of an expected utility function representation is proved. We discuss the notions of risk aversion, risk premium and certainty equivalent and characterize stochastic dominance criteria for comparing random variables. The chapter ends with a discussion of mean-variance preferences and their relation with stochastic dominance and expected utility.

References

  1. 41.
    Allais, M. (1953) Le comportement de l’homme rationnel devant le risque, critique des postulates et axioms de l’école americaine. Econometrica, 21:503–546.MathSciNetCrossRefMATHGoogle Scholar
  2. 72.
    Anscombe, F. and Aumann, R. (1963) A definition of subjective probability. Annals of Mathematical Statistics, 34:199–205.MathSciNetCrossRefMATHGoogle Scholar
  3. 78.
    Arrow, K. (1970) Essays, in the Theory of Risk Bearing. North-Holland, Amsterdam.MATHGoogle Scholar
  4. 395.
    Chamberlain, G. (1983) A characterization of the distributions that imply mean-variance utility functions. Journal of Economic Theory, 29:185–201.MathSciNetCrossRefMATHGoogle Scholar
  5. 448.
    Chung, K. L. (1979) Elementary Probability Theory with Stochastic Processes. Springer, New York.CrossRefMATHGoogle Scholar
  6. 537.
    De Finetti, B. (1952) Sulla preferibilità. Giornale degli Economisti and Annali di Economia, 11:685–709.Google Scholar
  7. 630.
    Eeckhoudt, L. and Gollier, C. (2000) The effects of change in risk on risk taking: A survey. Mimeo.Google Scholar
  8. 706.
    Fishburn, P. (1970) Utility Theory for Decision Making. Wiley, New York.MATHGoogle Scholar
  9. 744.
    Friedman, M. and Savage, L. (1948) The utility analysis of choice involving risk. Journal of Political Economy, 56:279–304.CrossRefGoogle Scholar
  10. 800.
    Gollier, C. (2001) The Economics of Risk and Time. MIT Press, Cambridge.MATHGoogle Scholar
  11. 803.
    Gollier, C. and Pratt, J. (1996) Risk vulnerability and tempering effect of background risk. Econometrica, 64:1109–1123.CrossRefMATHGoogle Scholar
  12. 938.
    Hens, T. and Rieger M.O. (2010) Financial Economics, Springer, Berlin/Heidelberg.CrossRefMATHGoogle Scholar
  13. 1000.
    Ingersoll, J. (1987) Theory of Financial Decision Making. Rowman & Littlefield, New Jersey.Google Scholar
  14. 1060.
    Kahneman, D. and Tversky, A. (1979) Prospect theory: an analysis of decision under risk. Econometrica, 47:263–291.CrossRefMATHGoogle Scholar
  15. 1089.
    Kihlstrom, R. and Mirman, L. (1974) Risk aversion with many commodities. Journal of Economic Theory, 8:361–368.MathSciNetCrossRefGoogle Scholar
  16. 1090.
    Kihlstrom, R. and Mirman, L. (1981) Constant, increasing, decreasing risk aversion with many commodities. Review of Economic Studies, 48:271–280.MathSciNetCrossRefMATHGoogle Scholar
  17. 1101.
    Kimball, M. (1993) Standard risk aversion. Econometrica, 61:589–611.MathSciNetCrossRefMATHGoogle Scholar
  18. 1136.
    Kreps, D. (1988) Notes on the Theory of Choice. Westview Press, Boulder.Google Scholar
  19. 1205.
    Levy, H. (2016) Stochastic Dominance: Investment Decision Making under Uncertainty, 3rd edition. Springer, Cham.CrossRefMATHGoogle Scholar
  20. 1310.
    Mas-Colell, A., Whinston, M. and Green, J. (1995) Microeconomic Theory. Oxford University Press.Google Scholar
  21. 1334.
    Meyer, J. (1987) Two-moment decision models and expected utility maximization. The American Economic Review, 77:421–430.Google Scholar
  22. 1389.
    Owen, J. and Rabinovitch, R. (1983) On the class of elliptical distributions and their applications to the theory of portfolio choice. Journal of Finance, 37:745–752.CrossRefGoogle Scholar
  23. 1432.
    Pratt, J. (1964) Risk aversion in the small and in the large. Econometrica, 32:122–136.CrossRefMATHGoogle Scholar
  24. 1433.
    Pratt, J. and Zeckauser, R. (1987) Proper risk aversion. Econometrica, 55:143–154.MathSciNetCrossRefMATHGoogle Scholar
  25. 1468.
    Ross, S. (1981) Some stronger measures of risk aversion in the small and large with applications. Econometrica, 49:621–638.MathSciNetCrossRefMATHGoogle Scholar
  26. 1472.
    Rothschild, M. and Stiglitz, J. (1970) Increasing risk I: a definition. Journal of Economic Theory, 2:225–243.MathSciNetCrossRefGoogle Scholar
  27. 1499.
    Savage, L. (1954) The Foundations of Statistics. Wiley, New York.MATHGoogle Scholar
  28. 1546.
    Simon, H. (1976) From substantive to procedural rationality. In Method and Appraisal in Economics, S. Latsis (ed.), Cambridge University Press.Google Scholar
  29. 1560.
    Sriboonchitta, S., Wong, W.-K., Dhompongsa, S. and Nguyen, H.T. (2010) Stochastic Dominance and Applications to Finance, Risk and Economics. CRC Press, Boca Raton.MATHGoogle Scholar
  30. 1596.
    Tobin, J. (1958) Liquidity preferences as behavior towards risk. Review of Economic Studies, 25:65–86.CrossRefGoogle Scholar
  31. 1632.
    Von Neumann, J. and Morgenstern, O. (1953) Theory of Games and Economic Behaviour. Princeton University Press.Google Scholar

Copyright information

© Springer-Verlag London Ltd. 2017

Authors and Affiliations

  • Emilio Barucci
    • 1
  • Claudio Fontana
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.Laboratoire de Probabilités et Modèles AléatoiresUniversité Paris Diderot (Paris 7)ParisFrance

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