A standard measure of risk and risk-value models

In this paper we propose a standard measure of risk that is based on the converted expected utility of normalized lotteries with zero-expected values. This measure of risk has many desirable properties that characterize the notion of risk. It is very general and includes many previously proposed measures of risk as special cases. Moreover, our standard measure of risk provides a preference-based and unified method for risk studies. Since the standard measure of risk is compatible with the measure of expected utility, it can be used explicitly or implicitly in an expected utility model. Under a condition called risk independence, a decision could be made by explicitly trading off between risk and value, which offers an alternative representation of the expected utility model, named the standard risk-value model. Finally, we discuss some other applications of the standard measure of risk and extensions of our risk-value tradeoff framework for descriptive decision making.