A measure of risk and a decision-making model based on expected utility and entropy

In this paper we extend the classical decision model under risk to a more general case, in which the state of nature corresponding to each risky action may have its own distribution. More specifically, we propose an expected utility–entropy (EU–E) measure of risk and a decision-making model based on expected utility and entropy. The EU–E measure of risk reflects an individual's intuitive attitude toward risk. The decision model incorporates the expected utility decision criterion as a special case. Using this decision model, a class of decision problems, which cannot be dealt with by applying the expected utility or mean–variance criterion reasonably, can be solved. Besides, some famous decision paradoxes can be interpreted. This decision model can either serve as a descriptive or a normative decision model involving risk.