Risk-seeking

In economics and finance, a risk-seeker or risk-lover is a person who has a preference for risk. While most investors are considered risk averse, one could view casino-goers as risk-seeking. If offered either $50 or a 50% each chance of either $100 or nothing, a risk-seeking person would prefer the gamble even though the gamble and the sure thing have the same expected value.

Risk-seeking behavior can be observed in the negative domain $x<0$ for prospect theory value functions, where the functions are convex for $x<0$ but concave for $x>0$.

The risk-seeking utility function

Choice under uncertainty is often characterized as the maximization of expected utility. Utility is often assumed to be a function of profit or final portfolio wealth, with a positive first derivative. The utility function whose expected value is maximized is convex for a risk-seeker, concave for a risk-averse agent, and linear for a risk-neutral agent. Its convexity in the risk-seeking case has the effect of causing a mean-preserving spread of any probability distribution of wealth outcomes to be preferred over the unspread distribution.