TY - UNPB

T1 - Decreasing Relative Risk Premium

AU - Hansen, Frank

N1 - JEL Classification: D8, G12

PY - 2006

Y1 - 2006

N2 - 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

AB - 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

KW - Faculty of Social Sciences

KW - expected utility theory

KW - preferences on lotteries

KW - relative risk premium

M3 - Working paper

BT - Decreasing Relative Risk Premium

PB - Department of Economics, University of Copenhagen

CY - Cph.

ER -