Deterministic Transformations of Random Variables and the Comparative Statics of Risk.

In this article, a general class of deterministic transformations that can be interpreted as changes in risk are identified. This provides a fourth characterization of a Rothschild-Stiglitz increase in risk. In addition, a particular subclass of these transformations, termed simple transformation, is shown to be well suited for comparative static analyses. This subclass contains as a special case the linear transformation used so often in the literature. A theorem is presented that generalizes the known comparative static results for large as well as small changes in risk. Copyright 1989 by Kluwer Academic Publishers