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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.

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. 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.
    2. 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.
    3. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    4. 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.
    5. 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.
    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 143-154, January.
    8. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    9. J. E. Stiglitz, 1969. "The Effects of Income, Wealth, and Capital Gains Taxation on Risk-Taking," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 83(2), pages 263-283.
    10. 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.
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    Cited by:

    1. Udo Broll & Antonio Roldán-Ponce & Jack Wahl, 2010. "Spatial Allocation of Capital: The Role of Risk Preferences," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(4), pages 389-398.
    2. Broll, Udo & Wahl, Jack E., 2011. "Liquidity constrained exporters and trade," Economics Letters, Elsevier, vol. 111(1), pages 26-29, April.
    3. Bieta, Volker & Broll, Udo & Siebe, Wilfried, 2014. "Collateral in banking policy: On the possibility of signaling," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 137-141.
    4. Broll, Udo & Guo, Xu & Welzel, Peter & Wong, Wing-Keung, 2015. "The banking firm and risk taking in a two-moment decision model," Economic Modelling, Elsevier, vol. 50(C), pages 275-280.
    5. Udo Broll & Sabine Hansen-Averlant, 2010. "Exchange rate volatility, international trade and labour demand," International Economics and Economic Policy, Springer, vol. 7(4), pages 423-436, December.
    6. Udo Broll & Kit Wong, 2013. "The firm under uncertainty: real and financial decisions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(2), pages 125-136, November.
    7. Broll, Udo & Wahl, Jack E., 2009. "Liquidity constrained exporters: Trade and futures hedging," Dresden Discussion Paper Series in Economics 17/09, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    8. Broll, Udo & Wong, Keith K.P., 2010. "The firm under uncertainty: capital structure and background risk," Dresden Discussion Paper Series in Economics 04/10, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    9. Broll, Udo & Egozcue, Martín & Wong, Wing-Keung, 2009. "Prospect theory and two moment model: the firm under price uncertainty," Dresden Discussion Paper Series in Economics 01/09, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.

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    Keywords

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    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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