Short answers, pulled from the story.
Risk aversion is the tendency to prefer outcomes with low uncertainty over those with high uncertainty, even when the uncertain option carries the same or higher average payoff. A risk-averse person will accept a guaranteed payment below the expected value of a gamble rather than face the uncertainty of the gamble itself.
The certainty equivalent is the smallest guaranteed dollar amount that leaves a person indifferent compared to an uncertain bet of the same average predicted value. For a risk-averse individual, the certainty equivalent is smaller than the expected value of the gamble, and the gap between the two is called the risk premium.
Kahneman and Tversky showed that risk preferences reverse systematically when losses replace gains. Most people choose a certain gain of 3,000 over an 80% chance of gaining 4,000, but prefer an 80% chance of losing 4,000 to a certain loss of 3,000. This reversal is most pronounced when small or large amounts and extreme probabilities are involved.
The Arrow-Pratt measure of absolute risk aversion, named after economists Kenneth Arrow and John W. Pratt, quantifies the curvature of a utility function in a way that is stable under rescaling. It is expressed in units of inverse dollars. A companion measure, the coefficient of relative risk aversion, is dimensionless and can be applied across different wealth levels and currencies.
Rabin's calibration theorem shows that a person who consistently refuses a 50-50 bet of losing $100 or gaining $110 from any wealth level would also refuse a 50-50 bet of losing $1,000 against gaining any finite amount. Rabin argued this implication is implausible, pointing to a fundamental limitation of expected utility theory for small-stakes decisions.
A 2009 study by Christopoulos and colleagues found that activity in the right inferior frontal gyrus correlates with risk aversion. Participants with higher risk premia showed stronger neural responses to safer options. Experiments that artificially modulated activity in that brain region caused participants to make more or less risk-averse choices accordingly.