attitude towards risk . risk averse , risk loving , risk neutral . expected utility. choice under u

consider an individual who has an aversion to risk, i.e. one who strongly dislikes risk. The utility function representing a risk-averse individual is not a straight line but rather is concave . Concavity of the function implies that its slope is decreasing, which in turn implies that this individual exhibits diminishing marginal utility for additional units of payoff. In other words, the risk-averse consumer is not willing to incur additional risk for the possibility of a higher valued payoff. Unlike his risk neutral counterpart, such an individual will not be indifferent between a risk-free and a risky activity, each of which has the same expected monetary value.
There are some individuals who actually prefer risky activities to risk-free ones. These individuals are called risk lovers possessing a risk preferring attitude. A utility function for such an agent convex . Note that the utility function becomes steeper as the agent’s payoff increases. Hence, a risk-preferring agent has increasing marginal utility for additional units of payoff represented by convex utility function. This simply means that the risk preferring individual is quite willing to take on additional risk for the possibility of a higher valued payoff.

A risk neutral person shows no preference between a certain income, and an uncertain income, given they both have equal expected value. In other words, he will be indifferent between a risky and a risk-free choice, if both result in same expected value to him.