Rankings of utility functions generated by simple n-th order risk-averse transformations are not partial orders, and therefore, do not yield reliable comparative statics predictions, except at the second order. Restrictions have been identified that rectify this deficiency at the third order...

We present two theorems that yield necessary and sufficient conditions for first and second-degree stochastic dominance deteriorations of background risk to increase risk aversion, prudence, temperance, and all higher degrees of aversion to foreground risk. We thus complete the program initiated...