Events

Prof. Wolfgang Pesendorfer
Theodore A. Wells ’29 Professor of Economics
Princeton University

We characterize all utility functions over risk prospects based on a cardinal utility index. Our main assumption, {\it  (Preference-Mixture) Certainty Independence}, is the counterpart of certainty-independence in the pure risk setting. We call preferences that have a have a cardinal utility index Lorenz expected utilities (LEUs) and show that they can be represented by a utility function that is the product of expected utility times one minus a general Gini index. We show that this last term quantifies the degree of first-order risk aversion. We then characterize a subset of LEU that we call rank-dependent disappointment averse (RDDA) preferences. These have three parameters: a probability transformation function, $\lambda$, a parameter $\beta\geq 0$ and a utility index, $u$ and include rank-dependent expected utility ($\beta=0$) and disappointment aversion ($\lambda$ is the identity function) as special cases. We characterize risk aversion for RDDA preferences. We provide a definition of Allais-prone behavior and show that an RDDA preference is Allais prone if and only if its $\lambda$ is a convex power function and either $\beta>0$ or $\lambda$ is strictly convex.  Finally, we show that RDDA preferences are a subset of   LEUs called probabilistically sophisticated maxmin expected utility preferences.