IDEAS home Printed from https://ideas.repec.org/p/kud/kuiedp/0621.html
   My bibliography  Save this paper

Decreasing Relative Risk Premium

Author

Listed:
  • Frank Hansen

    (Department of Economics, University of Copenhagen)

Abstract

We consider the risk premium demanded by a decision maker with wealth x in order to be indifferent between obtaining a new level of wealth y1 with certainty, or to participate in a lottery which either results in unchanged present wealth or a level of wealth y2 > y1. We define the relative risk premium as the quotient between the risk premium and the increase in wealth y1–x which the decision maker puts on the line by choosing the lottery in place of receiving y1 with certainty. We study preferences such that the relative risk premium is a decreasing function of present wealth, and we determine the corresponding class of utility functions which has several attractive properties and contains functions frequently used in the literature, including the power utility functions. The functions in the class are automatically continuously differentiable, and we characterize them in several ways. Decreasing relative risk premium in the small implies decreasing relative risk premium in the large, and decreasing relative risk premium everywhere implies risk aversion. We finally show that preferences with decreasing relative risk premium may be equivalently expressed in terms of certain preferences on risky lotteries.

Suggested Citation

  • Frank Hansen, 2006. "Decreasing Relative Risk Premium," Discussion Papers 06-21, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:0621
    as

    Download full text from publisher

    File URL: http://www.econ.ku.dk/Research/Publications/pink/2006/0621.pdf
    Download Restriction: no

    File URL: http://www.econ.ku.dk/english/research/publications/wp/2006/0621New.pdf/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lars Tyge Nielsen, 2006. "Monotone Risk Aversion," Studies in Economic Theory, in: Christian Schultz & Karl Vind (ed.), Institutions, Equilibria and Efficiency, chapter 17, pages 317-329, Springer.
    2. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    3. Quiggin, John & Chambers, Robert G, 1998. "Risk Premiums and Benefit Measures for Generalized-Expected-Utility Theories," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 121-137, November.
    Full references (including those not matched with items on IDEAS)

    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. Malevergne, Y. & Rey, B., 2009. "On cross-risk vulnerability," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 224-229, October.
    2. Angrisani, Marco & Atella, Vincenzo & Brunetti, Marianna, 2018. "Public health insurance and household portfolio Choices: Unravelling financial “Side Effects” of Medicare," Journal of Banking & Finance, Elsevier, vol. 93(C), pages 198-212.
    3. Gollier, Christian, 2002. "Time Horizon and the Discount Rate," Journal of Economic Theory, Elsevier, vol. 107(2), pages 463-473, December.
    4. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    5. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again," Econometrica, Econometric Society, vol. 89(1), pages 475-506, January.
    6. Zeckhauser, Richard Jay & Tran, Ngoc-Khanh, 2011. "The Behavior of Savings and Asset Prices When Preferences and Beliefs are Heterogeneous," Scholarly Articles 5027955, Harvard Kennedy School of Government.
    7. Haliassos, Michael & Hassapis, Christis, 2001. "Non-expected Utility, Saving and Portfolios," Economic Journal, Royal Economic Society, vol. 111(468), pages 69-102, January.
    8. Mario Maggi & Umberto Magnani & Mario Menegatti, 2006. "On the relationship between absolute prudence and absolute risk aversion," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 29(2), pages 155-160, November.
    9. Robert G. Chambers & John Quiggin, 2007. "Dual Approaches to the Analysis of Risk Aversion," Economica, London School of Economics and Political Science, vol. 74(294), pages 189-213, May.
    10. Letendre, Marc-Andre & Smith, Gregor W., 2001. "Precautionary saving and portfolio allocation: DP by GMM," Journal of Monetary Economics, Elsevier, vol. 48(1), pages 197-215, August.
    11. Luc Arrondel & Fr餩rique Savignac, 2015. "Risk management, housing and stockholding," Applied Economics, Taylor & Francis Journals, vol. 47(39), pages 4208-4227, August.
    12. Broll, Udo & Roldán-Ponce, Antonio & Wahl, Jack E., 2010. "Spatial allocation of capital: The role of risk preferences," Dresden Discussion Paper Series in Economics 03/10, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    13. Lisa L. Posey & Vickie Bajtelsmit, 2017. "Insurance and Endogenous Bankruptcy Risk: When is it Rational to Choose Gambling, Insurance, and Potential Bankruptcy?," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 42(1), pages 15-40, March.
    14. Röthig, Andreas, 2008. "The Impact of Backwardation on Hedgers' Demand for Currency Futures Contracts: Theory versus Empirical Evidence," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 35698, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    15. Luigi Guiso & Monica Paiella, 2008. "Risk Aversion, Wealth, and Background Risk," Journal of the European Economic Association, MIT Press, vol. 6(6), pages 1109-1150, December.
    16. Padmaja Ayyagari & Daifeng He, 2017. "The Role of Medical Expenditure Risk in Portfolio Allocation Decisions," Health Economics, John Wiley & Sons, Ltd., vol. 26(11), pages 1447-1458, November.
    17. Massimiliano Caporin & Grégory M. Jannin & Francesco Lisi & Bertrand B. Maillet, 2014. "A Survey On The Four Families Of Performance Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 28(5), pages 917-942, December.
    18. Denuit, Michel M. & Eeckhoudt, Louis & Schlesinger, Harris, 2013. "When Ross meets Bell: The linex utility function," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 177-182.
    19. Michael Haliassos & Alexander Michaelides, 2003. "Portfolio Choice and Liquidity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(1), pages 143-177, February.
    20. Irina Georgescu & Jani Kinnunen, 2013. "A risk approach by credibility theory," Fuzzy Information and Engineering, Springer, vol. 5(4), pages 399-416, December.

    More about this item

    Keywords

    expected utility theory; relative risk premium; preferences on lotteries;
    All these keywords.

    JEL classification:

    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:kud:kuiedp:0621. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/okokudk.html .

    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: Thomas Hoffmann (email available below). General contact details of provider: https://edirc.repec.org/data/okokudk.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.