IDEAS home Printed from https://ideas.repec.org/a/kap/rqfnac/v51y2018i3d10.1007_s11156-017-0688-z.html
   My bibliography  Save this article

Alternative utility functions: review, analysis and comparison

Author

Listed:
  • Arie Harel

    (City University of New York (CUNY))

  • Jack Clark Francis

    (City University of New York (CUNY))

  • Giora Harpaz

    (City University of New York (CUNY))

Abstract

The paper reviews the development of von Neumann and Morgenstern (vNM) utility theory. Kahneman and Tversky’s (KT’s) prospect theory is introduced. The vNM utility function is compared and contrasted with KT’s value function. We prove the uniqueness of two popular utility functions. First, we show that all power utility functions possess constant RRA. And, we show that all exponential utility functions have constant ARA. The paper concludes by discussing applications, strengths and weaknesses of various utility functions.

Suggested Citation

  • Arie Harel & Jack Clark Francis & Giora Harpaz, 2018. "Alternative utility functions: review, analysis and comparison," Review of Quantitative Finance and Accounting, Springer, vol. 51(3), pages 785-811, October.
    • Handle: RePEc:kap:rqfnac:v:51:y:2018:i:3:d:10.1007_s11156-017-0688-z
    DOI: 10.1007/s11156-017-0688-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11156-017-0688-z
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11156-017-0688-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nicholas Barberis & Wei Xiong, 2009. "What Drives the Disposition Effect? An Analysis of a Long‐Standing Preference‐Based Explanation," Journal of Finance, American Finance Association, vol. 64(2), pages 751-784, April.
    2. Kraus, Alan & Litzenberger, Robert H, 1975. "Market Equilibrium in a Multiperiod State Preference Model with Logarithmic Utility," Journal of Finance, American Finance Association, vol. 30(5), pages 1213-1227, December.
    3. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    4. Adrian Bruhin & Helga Fehr-Duda & Thomas Epper, 2010. "Risk and Rationality: Uncovering Heterogeneity in Probability Distortion," Econometrica, Econometric Society, vol. 78(4), pages 1375-1412, July.
    5. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    6. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    7. Milton Friedman, 1957. "Introduction to "A Theory of the Consumption Function"," NBER Chapters, in: A Theory of the Consumption Function, pages 1-6, National Bureau of Economic Research, Inc.
    8. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    9. Sundaresan, Mahadevan, 1983. "Constant Absolute Risk Aversion Preferences and Constant Equilibrium Interest Rates," Journal of Finance, American Finance Association, vol. 38(1), pages 205-212, March.
    10. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    11. Cho, Jaeho & Frances, Jack Clark, 1994. "Asset pricing implications of a non-expected recursive utility function: A review," International Review of Financial Analysis, Elsevier, vol. 3(1), pages 19-35.
    12. Milton Friedman, 1957. "A Theory of the Consumption Function," NBER Books, National Bureau of Economic Research, Inc, number frie57-1.
    13. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60(2), pages 151-151.
    14. Chin‐Wen Hsln & Jerry Kuo & Cheng‐Few Lee, 1994. "A new measure to compare the hedging effectiveness of foreign currency futures versus options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 14(6), pages 685-707, September.
    15. Peter P. Wakker, 2008. "Explaining the characteristics of the power (CRRA) utility family," Health Economics, John Wiley & Sons, Ltd., vol. 17(12), pages 1329-1344, December.
    16. Brown, David P & Gibbons, Michael R, 1985. "A Simple Econometric Approach for Utility-based Asset Pricing Models," Journal of Finance, American Finance Association, vol. 40(2), pages 359-381, June.
    17. Andrea Frazzini, 2006. "The Disposition Effect and Underreaction to News," Journal of Finance, American Finance Association, vol. 61(4), pages 2017-2046, August.
    18. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56(4), pages 279-279.
    19. Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, vol. 65(5), pages 900-922, December.
    20. Nawrocki, David & Viole, Fred, 2014. "Behavioral finance in financial market theory, utility theory, portfolio theory and the necessary statistics: A review," Journal of Behavioral and Experimental Finance, Elsevier, vol. 2(C), pages 10-17.
    21. Kroll, Yoram & Levy, Haim & Markowitz, Harry M, 1984. "Mean-Variance versus Direct Utility Maximization," Journal of Finance, American Finance Association, vol. 39(1), pages 47-61, March.
    22. Markowitz, Harry M, 1991. "Foundations of Portfolio Theory," Journal of Finance, American Finance Association, vol. 46(2), pages 469-477, June.
    23. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-317, June.
    24. repec:bla:jfinan:v:53:y:1998:i:5:p:1775-1798 is not listed on IDEAS
    25. Karson, Marvin J & Cheng, David C & Lee, Cheng F, 1995. "Sampling Distribution of the Relative Risk Aversion Estimator: Theory and Applications," Review of Quantitative Finance and Accounting, Springer, vol. 5(1), pages 43-54, March.
    26. Milton Friedman & Anna J. Schwartz, 1963. "A Monetary History of the United States, 1867–1960," NBER Books, National Bureau of Economic Research, Inc, number frie63-1.
    27. Mao-Wei Hung & Jr-Yan Wang, 2005. "Asset Prices Under Prospect Theory and Habit Formation," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 1-29.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jack Clark Francis, 2021. "Reformulating prospect theory to become a von Neumann–Morgenstern theory," Review of Quantitative Finance and Accounting, Springer, vol. 56(3), pages 965-985, April.
    2. Yonit Barron & Chananel Benshimol, 2024. "Emergency Supply Alternatives for a Storage Facility of a Repairable Multi-Component System," Mathematics, MDPI, vol. 12(17), pages 1-33, August.
    3. Andreas Karathanasopoulos & Chia Chun Lo & Xiaorong Ma & Zhenjiang Qin, 2021. "Maintaining cost and ruin probability," Review of Quantitative Finance and Accounting, Springer, vol. 57(2), pages 759-793, August.
    4. Barron, Yonit, 2023. "A stochastic card balance management problem with continuous and batch-type bilateral transactions," Operations Research Perspectives, Elsevier, vol. 10(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jakusch, Sven Thorsten, 2017. "On the applicability of maximum likelihood methods: From experimental to financial data," SAFE Working Paper Series 148, Leibniz Institute for Financial Research SAFE, revised 2017.
    2. Haim Levy, 2010. "The CAPM is Alive and Well: A Review and Synthesis," European Financial Management, European Financial Management Association, vol. 16(1), pages 43-71, January.
    3. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    4. Jack Clark Francis, 2021. "Reformulating prospect theory to become a von Neumann–Morgenstern theory," Review of Quantitative Finance and Accounting, Springer, vol. 56(3), pages 965-985, April.
    5. Sonntag, Dominik, 2018. "Die Theorie der fairen geometrischen Rendite [The Theory of Fair Geometric Returns]," MPRA Paper 87082, University Library of Munich, Germany.
    6. Nicholas C. Barberis, 2013. "Thirty Years of Prospect Theory in Economics: A Review and Assessment," Journal of Economic Perspectives, American Economic Association, vol. 27(1), pages 173-196, Winter.
    7. Michał Lewandowski, 2017. "Prospect Theory Versus Expected Utility Theory: Assumptions, Predictions, Intuition and Modelling of Risk Attitudes," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(4), pages 275-321, December.
    8. Levy, Moshe & Nir, Adi Rizansky, 2012. "The utility of health and wealth," Journal of Health Economics, Elsevier, vol. 31(2), pages 379-392.
    9. Nicholas C. Barberis, 2012. "Thirty Years of Prospect Theory in Economics: A Review and Assessment," NBER Working Papers 18621, National Bureau of Economic Research, Inc.
    10. Hooi Hooi Lean & Michael McAleer & Wing-Keung Wong, 2013. "Risk-averse and Risk-seeking Investor Preferences for Oil Spot and Futures," Documentos de Trabajo del ICAE 2013-31, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Aug 2013.
    11. Chorvat, Terrence, 2006. "Taxing utility," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 35(1), pages 1-16, February.
    12. Lean, Hooi Hooi & McAleer, Michael & Wong, Wing-Keung, 2015. "Preferences of risk-averse and risk-seeking investors for oil spot and futures before, during and after the Global Financial Crisis," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 204-216.
    13. Epper, Thomas & Fehr-Duda, Helga, 2017. "A Tale of Two Tails: On the Coexistence of Overweighting and Underweighting of Rare Extreme Events," Economics Working Paper Series 1705, University of St. Gallen, School of Economics and Political Science.
    14. W. Wong & R. Chan, 2008. "Prospect and Markowitz stochastic dominance," Annals of Finance, Springer, vol. 4(1), pages 105-129, January.
    15. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.
    16. Wang, Huijun & Yan, Jinghua & Yu, Jianfeng, 2017. "Reference-dependent preferences and the risk–return trade-off," Journal of Financial Economics, Elsevier, vol. 123(2), pages 395-414.
    17. Georgalos, Konstantinos & Paya, Ivan & Peel, David A., 2021. "On the contribution of the Markowitz model of utility to explain risky choice in experimental research," Journal of Economic Behavior & Organization, Elsevier, vol. 182(C), pages 527-543.
    18. Willem H. Buiter, 2003. "James Tobin: An Appreciation of his Contribution to Economics," Economic Journal, Royal Economic Society, vol. 113(491), pages 585-631, November.
    19. Haim Levy & Enrico G. De Giorgi & Thorsten Hens, 2012. "Two Paradigms and Nobel Prizes in Economics: a Contradiction or Coexistence?," European Financial Management, European Financial Management Association, vol. 18(2), pages 163-182, March.
    20. Arvanitis, Stelios & Scaillet, Olivier & Topaloglou, Nikolas, 2020. "Spanning analysis of stock market anomalies under prospect stochastic dominance," Working Papers unige:134101, University of Geneva, Geneva School of Economics and Management.

    More about this item

    Keywords

    von Neumann–Morgenstern (vNM) utility theory; Expected utility theory; Kahneman and Tversky (KT); Prospect theory; Framing; Loss aversion; Risk aversion; Risk taking; Absolute risk aversion (ARA); Relative risk aversion (RRA); Subjective probabilities; Decision weights; Objective probabilities; Probability weighting;
    All these keywords.

    JEL classification:

    • G02 - Financial Economics - - General - - - Behavioral Finance: Underlying Principles
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:rqfnac:v:51:y:2018:i:3:d:10.1007_s11156-017-0688-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.