# Risk

**DOI:**https://doi.org/10.1007/1-4020-0611-X_897

The risk of a decision *d* is the expected value of the loss incurred using *d* taken over all possible states of nature. A risk averse person is one who prefers to behave conservatively. A decision maker (DM) is said to be risk averse if the DM prefers the expected consequence of a nondegenerate lottery to that lottery (a nondegenerate lottery is one where no single consequence has a probability of one of occurring). A DM is risk averse if and only if the DM's utility function is concave. In contrast, a risk prone person is one who does not prefer to behave conservatively. A DM is said to be risk prone if the DM prefers any nondegenerate lottery to the expected consequences of that lottery. A DM is risk prone if and only if the DM's utility function is convex. Finally, a DM is risk neutral, if and only if the DM's utility function is linear. Lottery; Risk assessment ; Utility theory.