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Decreasing Relative Risk Premium

Author

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  • 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
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    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. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    3. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
    4. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    5. Ross, Stephen A, 1981. "Some Stronger Measures of Risk Aversion in the Small and the Large with Applications," Econometrica, Econometric Society, vol. 49(3), pages 621-638, May.
    6. 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)

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    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

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