This chapter deals with prospect theory, which generalizes RDU by incorporating loss aversion. It thus integrates utility curvature, probabilistic sensitivity, and loss aversion, the three components of risk attitude.

A symmetry about 0 underlying prospect theory

It is plausible that utility has a kink at zero, and exhibits different properties for gains than for losses. Formally, for a fixed reference point these properties could also be modeled by rank-dependent utility, in the same way as §8.3 does not entail a real departure from final wealth models and expected utility. Prospect theory does generalize rank-dependent utility in one formal respect also for the case of one fixed reference point: It allows for different probability weighting for gains than for losses. Thus, risk attitudes can be different for losses than for gains in every respect.

It is plausible that sensitivity to outcomes and probabilities exhibits symmetries about the reference point. To illustrate this point, we first note that the utility difference U(1020) − U(1010) is usually smaller than the utility difference U(20) − U(10) because the former concerns outcomes farther remote from 0, leading to concave utility for gains. A symmetric reasoning for losses suggests that the utility difference U(−1010) − U(−1020) will be perceived as smaller than the utility difference U(−10) − U(−20). For the former difference, the losses are so big that 10 more does not matter much. This argument suggests convex rather than concave utility for losses, in agreement with many empirical findings (§9.5).