A nonsmooth approach to nonexpected utility theory under risk

We consider concave and Lipschitz continuous preference functionals over monetary lotteries. We show that they possess an envelope representation, as the minimum of a bounded family of continuous vN-M preference functionals. This allows us to use an envelope theorem to show that results from local utility analysis still hold in our setting, without any further differentiability assumptions on the preference functionals. We introduce a class of (possibly nonsmooth) concave and Lipschitz continuous preference functionals that allow us to disentangle the concepts of risk aversion and diminishing marginal utility for money. We then examine, while keeping the marginal utility of wealth fixed, the effect of increased risk aversion in portfolio and asset pricing problems, where we get intuitive results that are not possible in expected utility theory. Finally, we provide an axiomatisation of a class of concave preference functionals that are Lipschitz. Chatterjee would like to thank the Human Capital Foundation for its support of the Penn State Department of Economics. We would also like to thank participants at RUD 2009 and other seminars for useful comments. Helpful suggestions were made by Philipp Sadowski, Fabio Maccheroni who also alerted us to his paper, and Edi Karni. Remaining errors are our own. †Pennsylvania State University ‡University of North Carolina, Chapel Hill