Infinite Horizon Stochastic Differential Utility

This note supplements Duffie and Epstein (1989). Existence and uniqueness of an infinite horizon stochastic differential utility function is proved. The issue of existence is analogous to that of stability of a non-linear feedback system. Stability is guaranteed by imposing a “uniform sector condition” on the “feedback function.” The basic properties of the finite horizon recursive utility presented by Duffle and Epstein generalize directly to the infinite horizon case._x000B_