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Power Risk Aversion Utility Functions

Author

Listed:
  • Danyang Xie

    (Department of Economics, Hong Kong University of Science and Technology
    International Monetary Fund)

Abstract

This paper introduces a new class of utility functions---the power risk aversion. It is shown that the CRRA and CARA utility functions are both in this class. The implications of the PRA utility functions are explored in the context of growth theory. In particular, it is found that economies facing a common real interest rate do not necessarily grow at the same rates if they start with different levels of capital stock. Thus diversity in growth performance across countries occurs even if these countries have access to perfect international capital markets. Potential applications of the PRA in asset pricing are considered.

Suggested Citation

  • Danyang Xie, 2000. "Power Risk Aversion Utility Functions," Annals of Economics and Finance, Society for AEF, vol. 1(2), pages 265-282, November.
    • Handle: RePEc:cuf:journl:y:2000:v:1:i:2:p:265-282
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    Cited by:

    1. Smith, William T. & Zhang, Qiang, 2007. "Asset pricing with multiplicative habit and power-expo preferences," Economics Letters, Elsevier, vol. 94(3), pages 319-325, March.
    2. Mark Kagan & Frederick Ploeg & Cees Withagen, 2015. "Battle for Climate and Scarcity Rents: Beyond the Linear-Quadratic Case," Dynamic Games and Applications, Springer, vol. 5(4), pages 493-522, December.
    3. Andrea Bigano & Mariaester Cassinelli & Anil Markandya & Fabio Sferra, 2010. "The Role of Risk Aversion and Lay Risk in the Probabilistic Externality Assessment for Oil Tanker Routes to Europe," Journal of Transport Economics and Policy, University of Bath, vol. 44(1), pages 93-118, January.
    4. William T. Smith & Qiang Zhang, 2006. "Asset Pricing With Multiplicative Habit and Power-Expo Preferences (Subsequently published in "Economics Letters", 2007, 94(3), 319-325. )," CARF F-Series CARF-F-070, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Soriano-Morales, Y. V. & Vallejo-Jiménez, Benjamín & Venegas-Martínez, Francisco, 2017. "Impact of the degree of relative risk aversion, the interest rate and the exchange rate depreciation on economic welfare in a small open economy," Panorama Económico, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 13(25), pages 7-24, Primer se.
    6. Samuel Mongrut Montalván, 2016. "Discount Rates for Seed Capital Investments," Working Papers 16-01, Centro de Investigación, Universidad del Pacífico.
    7. Spreeuw, Jaap, 2014. "Archimedean copulas derived from utility functions," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 235-242.
    8. Denis Conniffe, 2007. "The Generalised Extreme Value Distribution as Utility Function," The Economic and Social Review, Economic and Social Studies, vol. 38(3), pages 275-288.
    9. Jack Meyer, 2010. "Representing risk preferences in expected utility based decision models," Annals of Operations Research, Springer, vol. 176(1), pages 179-190, April.
    10. Denis Conniffe, 2007. "The Flexible Three Parameter Utility Function," Annals of Economics and Finance, Society for AEF, vol. 8(1), pages 57-63, May.
    11. Angus Macdonald & Pradip Tapadar, 2010. "Multifactorial Genetic Disorders and Adverse Selection: Epidemiology Meets Economics," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(1), pages 155-182, March.
    12. de Brauw, Alan & Eozenou, Patrick, 2014. "Measuring risk attitudes among Mozambican farmers," Journal of Development Economics, Elsevier, vol. 111(C), pages 61-74.
    13. Bahaji, Hamza, 2012. "De l’évaluation des stock options en « juste valeur » : apport de l’approche comportementale," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/10710 edited by Casta, Jean-François.
    14. Conniffe, Denis, 2008. "Generalised Means of Simple Utility Functions with Risk Aversion," The Economic and Social Review, Economic and Social Studies, vol. 39(1), pages 1-12.
    15. Ruo Jia & Zenan Wu, 2019. "Insurer commitment and dynamic pricing pattern," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 44(1), pages 87-135, March.
    16. Bostian, AJ A. & Heinzel, Christoph, 2024. "Precautionary saving under recursive preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 228(C).
    17. Ruo Jia & Zenan Wu, 2019. "Insurer commitment and dynamic pricing pattern," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 44(1), pages 87-135, March.
    18. Charles E. Phelps, 2024. "A user’s guide to economic utility functions," Journal of Risk and Uncertainty, Springer, vol. 69(3), pages 235-280, December.
    19. Mitra, Tapan & Roy, Santanu, 2012. "Sustained positive consumption in a model of stochastic growth: The role of risk aversion," Journal of Economic Theory, Elsevier, vol. 147(2), pages 850-880.
    20. Ferro, Giuseppe M. & Kovalenko, Tatyana & Sornette, Didier, 2021. "Quantum decision theory augments rank-dependent expected utility and Cumulative Prospect Theory," Journal of Economic Psychology, Elsevier, vol. 86(C).

    More about this item

    Keywords

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    JEL classification:

    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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