Unique solutions for stochastic recursive utilities

We study unique and globally attracting solutions of a general nonlinear stochastic equation, widely used in Finance and Macroeconomics and closely related to stochastic Koopmans equations. The equation is specified by a temporal aggregator W and a certainty equivalent operator . The main contribution of the paper is the introduction of the new class of Thompson aggregators. Other contributions of the paper are: (i) a detailed analysis of quasi-arithmetic operators that generalize those of Kreps and Porteus (1978) [18]; (ii) a clarification of the nature and properties of the stochastic recursive preferences that underlie Koopmans equations.