Smooth Ambiguity Aversion Toward Small Risks and Continuous-Time Recursive Utility

Assuming Brownian/Poisson uncertainty, a certainty equivalent (CE) based on the smooth second-order expected utility of Klibanoff, Marinacci, and Mukerji (Econometrica, 2005) is shown to be approximately equal to an expected-utility CE. As a consequence, the corresponding continuous-time recursive utility form is the same as for Kreps-Porteus utility. The analogous conclusions are drawn for a smooth divergence CE, based on a formulation of Maccheroni, Marinacci, and Rustichini (Econometrica, 2006), but only under Brownian uncertainty. Under Poisson uncertainty, a smooth divergence CE can be approximated with an expected-utility CE if and only if it is of the entropic type. A non-entropic divergence CE results in a new class of continuous-time recursive utilities that price Brownian and Poissonian risks differently. ∗Kellogg School of Management, Department of Finance, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208. I am grateful for helpful discussions with Nabil Al-Najjar, Larry Epstein, Ronald Gindrat, Lars Hansen, Soohun Kim, Peter Klibanoff, Fabio Maccheroni, Mark Machina, Massimo Marinacci, Jianjun Miao, Sujoy Mukerji, Dimitris Papanikolaou and Viktor Todorov. I am especially thankful for the feedback I have received from Christian Hellwig, Monika Piazzesi and Mark Schroder. I’m responsible for any errors. The latest version of this article, along with the Appendix and computer code for the example of Section 2, can be downloaded at http://www.kellogg.northwestern.edu/faculty/skiadas/home.htm