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Utility Functions of Equivalent Form and the Effect of Parameter Changes on Optimum Decision Making

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  • Broll, Udo
  • Battermann, Harald L.
  • Wahl, Jack E.
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    Abstract

    We derive a class of utility functions that are equivalent with respect to a well-defined functional form. We study the case of constant relative risk aversion (of some order) to investigate on different equivalence relations in order to determine the, possibly infinite, number of equivalence classes when utility functions satisfy a specific form. Then we apply our results to standard applications in economics and finance, for example, to the effect of price volatility on optimum hedging. --

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    File URL: http://econstor.eu/bitstream/10419/22729/1/DDPE200602.pdf
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    Bibliographic Info

    Paper provided by Dresden University of Technology, Faculty of Business and Economics, Department of Economics in its series Dresden Discussion Paper Series in Economics with number 02/06.

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    Date of creation: 2006
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    Handle: RePEc:zbw:tuddps:0206

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    Postal: 01062 Dresden
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    Fax: ++49 351 463 7739
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    Web page: http://www.tu-dresden.de/wiwi/
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    Keywords: equivalence class; risk aversion; sensitivity analysis;

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    1. Stiglitz, Joseph E, 1969. "The Effects of Income, Wealth, and Capital Gains Taxation on Risk-Taking," The Quarterly Journal of Economics, MIT Press, vol. 83(2), pages 263-83, May.
    2. Broll, Udo & Wahl, Jack E. & Zilcha, Itzhak, 1995. "Indirect hedging of exchange rate risk," Journal of International Money and Finance, Elsevier, vol. 14(5), pages 667-678, October.
    3. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    4. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    5. Broll, Udo & Wahl, Jack E. & Zilcha, Itzhak, 1999. "Hedging exchange rate risk: The multiperiod case," Research in Economics, Elsevier, vol. 53(4), pages 365-380, December.
    6. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    7. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-54, January.
    8. Chew, Hong Soo & Herk, Leonard F., 1996. "Incremental Risk Aversion and Diversification Preference," Journal of Economic Theory, Elsevier, vol. 70(1), pages 180-200, July.
    9. Eckwert, Bernhard, 1993. "Allocative effects of financial assets and the long run neutrality of money when markets are incomplete," European Economic Review, Elsevier, vol. 37(1), pages 75-95, January.
    10. Robert Chambers & Rolf Färe & John Quiggin, 2004. "Jointly radial and translation homothetic preferences: generalized constant risk aversion," Economic Theory, Springer, vol. 23(3), pages 689-699, March.
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