Smooth ambiguity aversion toward small risks and continuous-time recursive utility

Assuming Brownian/Poisson uncertainty, a certainty equivalent {eth}CE{Thorn} based on the smooth second-order expected utility of Klibanoff, Marinacci, and Mukerji is shown to be approximately equal to an expectedutility 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, 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 nonentropic divergence CE results in a new class of continuous-time recursive utilities that price Brownian and Poissonian risks differently.