Some conditions for the equivalence between risk aversion, prudence and temperance

We study relationships between different aspects of risk preferences. We show that, under the assumptions of non-satiation and bounded marginal utility, some additional conditions on the asymptotic behaviour of the indices of relative prudence and relative temperance ensure that risk aversion, prudence and temperance are equivalent. Similar conclusions are derived for higher-degree risk aversion. Moreover, some links between indices of relative risk aversion of different degrees are derived. The implications of these results for several economic problems which involve risk changes are discussed.