Decreasing relative risk premium
نویسنده
چکیده
We consider the risk premium π demanded by a decision maker with present 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 wealth x or a level of wealth y2 > y1. We then define the relative risk premium λ as the quotient between π 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 introduce the notion of partial risk neutral preferences on binary lotteries and show that partial risk neutrality is equivalent to preferences with decreasing relative risk premium. JEL classification: D8 and G12.
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