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. It is quite hard to distinguish risk seeker from risk indifferent because both make risky calls.

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.

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