Advertisement

Stochastic Dominance for the Class of Completely Monotonic Utility Functions

  • G. A. Whitmore

Abstract

According to the expected utility axioms, a decision maker with utility function u(x) for wealth x assigns the following subjective value to an uncertain prospect with cumulative distribution function F(x).
$$ E(u;F) = \smallint _0^\infty u(x)dF(x) $$
(1)
It is assumed here that wealth level x is positive and that prospect F has moments of all orders.

Keywords

Utility Function Stochastic Dominance Extremal Function Absolute Risk Aversion Convex Linear Combination 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blackwell, D., and M.A. Girshick, Theory of Games and Statistical Decisions. New York: Wiley, 1954.Google Scholar
  2. Brumelle, S.L., and R.G. Vickson, “A Unified Approach to Stochastic Dominance.” In Stochastic Optimization Models in Finance, eds. W.T. Ziemba and R.G. Vickson. New York: Academic Press, 1975.Google Scholar
  3. Fishburn, P.C., Decision and Value Theory. New York: Wiley, 1964.Google Scholar
  4. Fishburn, P.C., and R.G. Vickson, “Theoretical Foundations of Stochastic Dominance.” In Stochastic Dominance, eds. G.A. Whitmore and M.C. Findlay. Lexington, Massachusetts: Heath, 1978.Google Scholar
  5. Hadar, J., and W.R. Russell, “Rules for Ordering Uncertain Prospects,” American Economic Review 59 (1969): 25–34.Google Scholar
  6. Hanoch, G., and H. Levy, “The Efficiency Analysis of Choices Involving Risk,” Review of Economic Studies 36 (1969): 335–346.CrossRefGoogle Scholar
  7. Hildreth, C., “Expected Utility of Uncertain Ventures,” Journal of the American Statistical Association 69 (1974): 9–17.CrossRefGoogle Scholar
  8. Jean, W.H., “The Geometric Mean and Stochastic Dominance,” Journal of Finance 35 (1980): 151–158.CrossRefGoogle Scholar
  9. Keeney, R.L., and H. Raiffa, Decisions with Multiple Objectives: Preferences and Value Tradeoffs. New York: Wiley, 1976.Google Scholar
  10. Levy, H., and Y. Kroll, “Ordering Uncertain Options with Borrowing and Lending,” Journal of Finance 33 (1978): 553–573.CrossRefGoogle Scholar
  11. Phelps, R.R., Lectures on Choquet’s Theorem. Princeton, New Jersey: D. Van Nostrand, 1966.Google Scholar
  12. Quirk, J.P., and R. Saposnik, “Admissibility and Measurable Utility Functions,” Review of Economic Studies 29 (1962): 140–146.CrossRefGoogle Scholar
  13. Rothschild, M., and J.E. Stiglitz, “Increasing Risk I: A Definition,” Journal of Economic Theory 2 (1970): 225–243.CrossRefGoogle Scholar
  14. Vickson, R.G., “Stochastic Dominance Tests for Decreasing Absolute Risk Aversion I: Discrete Random Variables,” Management Science, Application Series, 21 (1975): 1438–1446.Google Scholar
  15. Vickson, R.G., “Stochastic Dominance Tests for Decreasing Absolute Risk Aversion II: General Random Variables,” Management Science, Application and Theory Series 23 (1977): 478–489.Google Scholar
  16. Whitmore, G.A., “Third-Degree Stochastic Dominance,” American Economic Review 60 (1970): 457–459.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • G. A. Whitmore
    • 1
  1. 1.McGill UniversityMontrealCanada

Personalised recommendations