Abstract: The study of decision-making under risk has been a major thrust of microeconomics and psychology in the last few decades. Both classical decision-making theory and prospect theory focus on the study of decision-making behavior, while the psychological mechanism under the decision-making has been in the dark. The latest and possibly most exciting frontier in this research area is the effort to understand the way in which neural processes mediate risk-taking behavior. Neuroscientists and their collaborators begin to apply modern neurophysiology methods to risk decision-making. The mechanisms and neural basis of framing effects that violate the invariance principle are presented and discussed from the following aspects: positive & negative framing, sure choice & risk option, risk aversion & risk seeking, and over-weighting low probabilities. Concluding remarks assess the future prospects of the cognitive neuroscience of decision-making under risk, such as decision-making under uncertainty and multiple play

Key words: decision-making under risk, framing effect, neural mechanism