Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T23:04:14.611Z Has data issue: false hasContentIssue false
  • English
  • Français

Inequalities with application in economic risk analysis

Published online by Cambridge University Press:  14 July 2016

Robert A. Agnew
Robert A. Agnew*
Affiliation:
Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio
Get access Rights & Permissions [Opens in a new window]

Abstract

Two sharp lower bounds for the expectation of a function of a non-negative random variable are obtained under rather weak hypotheses regarding the function, thus generalizing two sharp upper bounds obtained by Brook for the moment generating function. The application of these bounds to economic risk analysis is discussed.

Keywords

TCHEBYCHEV INEQUALITIESMETHOD OF MARKOVCONVEX FUNCTIONSECONOMIC RISK ANALYSISEXPECTED UTILITYMEAN VARIANCE LOWER BOUNDS
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 441 - 444
Copyright
Copyright © Applied Probability Trust 1972 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Arrow, K. J. (1965) Aspects of the Theory of Risk-Bearing. Yrjö Jahnssonin Säätiö, Helsinki.Google Scholar
[2] Borch, K. H. (1968) The Economics of Uncertainty. Princeton University Press, Princeton, N. J.Google Scholar
[3] Brook, D. (1966) Bounds for moment generating functions and for extinction probabilities. J. Appl. Prob. 3, 171–178.Google Scholar
[4] Bruckner, A. M. and Ostrow, E. (1962) Some function classes related to the class of convex functions. Pacific J. Math. 12, 1203–1215.CrossRefGoogle Scholar
[5] Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. II. (2nd ed.). Wiley, New York.Google Scholar
[6] Hanoch, G. and Levy, H. (1969) The efficiency analysis of choices involving risk. Rev. Econ. Stud. 36, 335–346.CrossRefGoogle Scholar
[7] Hardy, G. H., Littlewood, J. E. and Pólya, G. (1952) Inequalities. (2nd ed.). Cambridge University Press, Cambridge.Google Scholar
[8] Kingman, J. F. C. (1963) On inequalities of the Tchebychev type. Proc. Camb. Phil. Soc. 59, 135–146.CrossRefGoogle Scholar
[9] Markowitz, H. M. (1959) Portfolio Selection. Wiley, New York.Google Scholar
[10] Mitrinovic, D. S. (1970) Analytic Inequalities. Springer-Verlag, Berlin.CrossRefGoogle Scholar
[11] Von Neumann, J. and Morgenstern, O. (1947) Theory of Games and Economic Behavior. (2nd ed.). Princeton University Press, Princeton, N.J. Google Scholar
[12] Pratt, J. W. (1964) Risk aversion in the small and in the large. Econometrica 32, 122–136.CrossRefGoogle Scholar
[13] Samuelson, P. A. (1970) The fundamental approximation theorem of portfolio analysis in terms of means, variances, and higher moments. Rev. Econ. Stud. 37, 537–542.CrossRefGoogle Scholar
[14] Tobin, J. (1958) Liquidity preference as behavior towards risk. Rev. Econ. Stud. 25, 65–86.CrossRefGoogle Scholar