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Decreasing Relative Risk Premium

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  • Frank Hansen

    (Department of Economics, University of Copenhagen)

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    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.

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    Bibliographic Info

    Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 06-21.

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    Length: 14 pages
    Date of creation: Nov 2006
    Date of revision:
    Handle: RePEc:kud:kuiedp:0621

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    Related research

    Keywords: expected utility theory; relative risk premium; preferences on lotteries;

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    1. Nielsen, Lars Tyge, 1997. "Monotone Risk Aversion," CEPR Discussion Papers 1651, C.E.P.R. Discussion Papers.
    2. 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 121-37, November.
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