Risk-aversion, prudence and temperance: A unified approach

Risk-aversion can be defined either by the negative sign of the second derivative of the utility function or by the rejection of any mean-preserving increase in risk. The more recent notions of prudence and temperance have so far been defined exclusively by the sign of the third and the fourth derivative of the utility function. In this paper we show that, as risk-aversion, prudence and temperance can also be interpreted as systematic attitudes towards transformation of a density function.