The Realization E↵ect: Risk-Taking After Realized Versus Paper Losses Appendix: For Online Publication

where V (r|r) = 0, v is concave, and > 1 implies loss aversion. Note that this implies that the value function V (x|r) is concave for gains (xi r) and convex for losses (xi < r). Under CPT, the probability weighting function w : [0, 1] ! [0, 1] transforms objective probabilities into decision weights ⇡. The weighting function w is assumed to satisfy the reflection property, assigning the same weight to a given gain-probability as to a given lossprobability (Prelec, 1998; Tversky and Kahneman, 1992). Unlike in the original prospect theory (Kahneman and Tversky, 1979), in CPT probability weighting is rank-dependent, such that