New results on the relationship among risk aversion, prudence and temperance

• Under non-satiation and bounded marginal utility, prudence implies risk aversion.
• Under non-satiation and bounded marginal utility, imprudence implies risk loving.
• Under non-satiation and bounded marginal utility, temperance implies prudence.
• Under non-satiation and bounded marginal utility, intemperance implies imprudence.
• Implications for increases in risk, in downside risk and in outer risk are discussed.

This note studies the relationships between different aspects of agent’s preferences toward risk. We show that, under the assumptions of non-satiation and bounded marginal utility, prudence implies risk aversion (imprudence implies risk loving) and that temperance implies prudence (intemperance implies imprudence). The implications of these results for comparing risks in the cases of increase in risk, increase in downside risk and increase in outer risk are discussed.

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