Relative Risk Aversion, Relative Prudence and Comparative Statics under Uncertainty: The Case of (mu,sigma)-Preferences

From the expected-utility approach, relative risk aversion being smaller than one and relative prudence being smaller than two emerge as preference restrictions that fully determine the optimal responses of decisions under uncertainty to certain shifts in probability distributions. We characterize the magnitudes of relative risk aversion and relative prudence in terms of the two-parameter, mean-standard deviation approach. We demonstrate that this characterization is instrumental in obtaining comparative static results in the two-parameter setting. We further relate our findings to the results in the expected-utility framework.