Donald C., Rudow (2005): Preferences and Increased Risk Aversion under a General Framework of Stochastic Dominance.
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This paper analyzes increased risk aversion in the presence of two risks. Necessary and sufficient conditions for increased risk aversion across the domain of the foreground risk are found for changes in both the foreground and background risks. Preferences that satisfy the necessary and sufficient conditions are determined through a lower bound on their measure of prudence. These bounds are found through second-degree spreads of a transformation of the background risk. The necessary and sufficient conditions demonstrate that for all second degree spreads of this nature, absolute temperance plays a central role in the necessary and sufficient conditions for increased risk aversion. The approach also demonstrates that changes in risk aversion under the general framework of stochastic dominating spreads can be explained by a weighted average of terms involving absolute prudence and absolute temperance. Once a general set of necessary and sufficient conditions have been found it is shown that for preferences that are decreasing absolute risk averse in the sense of Ross, increased risk aversion due to changes in the background risk within this framework is equivalent to Ross risk vulnerability. The general conditions also find necessary and sufficient conditions for preferences to be properly risk averse toward patent increases in risk.
|Item Type:||MPRA Paper|
|Original Title:||Preferences and Increased Risk Aversion under a General Framework of Stochastic Dominance|
|Keywords:||Stochastic dominance, increased risk aversion, background risk, transformations, patent increase in risk, prudence, proper risk aversion, risk vulnerability|
|Subjects:||D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D84 - Expectations; Speculations
D - Microeconomics > D0 - General > D01 - Microeconomic Behavior: Underlying Principles
D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - General
|Depositing User:||Donald C. Rudow|
|Date Deposited:||11. Sep 2012 11:33|
|Last Modified:||18. Sep 2014 06:24|
Diamond, P. and Stiglitz, J. “Risk and Risk Aversion,” Journal of Economic Theory, 8 (1974), 337-360.
Eeckhoudt, L., Gollier, C. and Schlesinger, H. “Changes in Background Risk and Risk Taking Behavior,” Econometrica, Vol. 64, No. 3 (May 1996), 683-689.
Gollier, C. “The Economics of Risk and Time.” MIT Press, Cambridge, MA 2001.
Gollier, C., and Pratt, J., “Risk Vulnerability and the Tempering Effects of Background Risk,” Econometrica, Vol. 64, No. 5 (1996), 1109-1123.
Hadar, J. and Russell, W., “Rules for Ordering Uncertain Prospects,” The American Economic Review, Vol. 59, No. 1 (1969), 25-34.
Keenan, D. and Snow, A. “Locally Greater Vulnerability to Background Risk,” Geneva Papers on Risk and Insurance Theory, Vol. 28 issue 2, (December 2003), 161-172.
Kihlstrom, R., Romer, D., and Williams, S. “Risk Aversion with Random Initial Wealth,” Econometrica, Vol. 49, No. 4 (July, 1981), 911-920.
Kimball, M. “Precautionary Saving in the Small and in the Large,” Econometrica, Vol. 58, No. 1 (Jan., 1990), 53-73.
Kimball, M., Precautionary Motives for Holding Assets, The New Palgrave Dictionary of Money and Finance. Vol. 3, Newman, P., Milgate, M. and Eatwell, J. eds., The Macmillan Press Limited, New York 1992, 158-161.
Kimball, M., “Standard Risk Aversion,” Econometrica, Vol. 61, No. 3 (May, 1993), 589-611.
Kirman, A.P. Measure Theory, “Handbook of Mathematical Economics.” Vol. I, Elsevier Science B.V., Amsterdam, (1981), 159-209.
Leshno, M., Levy, H., and Spector, Y. “A Comment on Rothschild and Stiglitz’s ‘Increasing Risk I: A Definition’,” Journal of Economic Theory, 77 (1997), 223-228.
Machina, M. and Pratt, J. “Increasing Risk: Some Direct Constructions,” Journal of Risk and Uncertainty, Vol. 14 (1997), 103-127.
Meyer, J. “Second Degree Stochastic Dominance with Respect to a Function,” International Economic Review, Vol. 18, No. 2 (June 1977).
Meyer, J., “Studies in the Economics of Uncertainty in Honor of Josef Hadar”, eds. Fomby, T and Seo, T., (1989)
Meyer, J. and Ormiston, M., “Deterministic Transformations of Random Variables and the Comparative Statics of Risk,” Journal of Risk and Uncertainty, Vol. 2, iss. 2, (June 1989), 179-188.
Müller, A. and Scarsini, M. “Stochastic Comparison of Random Vectors with a Common Copula,” Mathematics of Operations Research, Vol. 26 No. 4 (Nov. 2001), 723-740.
Pratt, J. “Risk Aversion in the Small and in the Large,” Econometrica, Vol. 32, ½ (Jan-April 1964), 122-136.
Pratt, J., “Aversion to One Risk in the Presence of Others,” Journal of Risk and Uncertainty, 1, (1988), 395-413.
Pratt, J., “The Logic of Partial Risk Aversion: Paradox Lost,” Journal of Risk and Uncertainty, 3, (1990), 105-13.
Pratt, J., and Zeckhauser, R. “Proper Risk Aversion,” Econometrica, Vol. 55 (Jan. 1987), 143-154.
Ross, S. “Some Stronger Measures of Risk Aversion in the Small and the Large with Applications,” Econometrica, Vol. 49, 3 (May, 1981), 621-638.
Rothschild, M. and Stiglitz, J. “Increasing Risk I: a Definition,” Journal of Economic Theory, 2 (1970), 225-243.
Rudin, W. “Principles of Mathematical Analysis.” 3rd ed., McGraw Hill, Inc., New York, 1976.
Sandmo, A. “On the Theory of the Competitive Firm under Price Uncertainty,” The American Economic Review, Vol. 61, No. 1 (March 1971), 65-73.
Spivak, M. “Calculus on Manifolds.” Perseus Books. Cambridge, 1965.