Diffidence Theorem, State-Dependent Preferences, and DARA

C. Gollier (The Economics of Risk and Time. Cambridge: MIT Press, 2001) has developed a standard technique based on the diffidence theorem. This theorem provides a very simple instrument to solve relatively sophisticated problems when preferences are state-independent. The object of this article is to show that the theorem is also very useful to derive significant results with state-dependent preferences. Using the reference set notion and an extension of the diffidence theorem, we establish formally necessary and sufficient conditions on the reference set, in order to obtain prudence and decreasing absolute risk aversion. Examples of DARA utility functions compatible with non-linear reference sets are presented in the Appendix.