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

Author

Listed:
  • Broll, Udo
  • Battermann, Harald L.
  • Wahl, Jack E.

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.

Suggested Citation

  • Broll, Udo & Battermann, Harald L. & Wahl, Jack E., 2006. "Utility Functions of Equivalent Form and the Effect of Parameter Changes on Optimum Decision Making," Dresden Discussion Paper Series in Economics 02/06, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
  • Handle: RePEc:zbw:tuddps:0206
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    References listed on IDEAS

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    1. 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.
    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. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    4. J. E. Stiglitz, 1969. "The Effects of Income, Wealth, and Capital Gains Taxation on Risk-Taking," The Quarterly Journal of Economics, Oxford University Press, vol. 83(2), pages 263-283.
    5. 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.
    6. Robert Chambers & Rolf Färe & John Quiggin, 2004. "Jointly radial and translation homothetic preferences: generalized constant risk aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 689-699, March.
    7. 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.
    8. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    9. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    10. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
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    More about this item

    Keywords

    equivalence class; risk aversion; sensitivity analysis;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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