Backward Nonlinear Expectation Equations

Building on an abstract framework for dynamic nonlinear expectations that comprises g-, G- and random G-expectations, we develop a theory of backward nonlinear expectation equations. We provide existence, uniqueness, and stability results and establish convergence of the associated discrete-time nonlinear aggregations. As an application, we construct continuous-time recursive utilities under ambiguity and identify the corresponding utility processes as limits of discrete-time recursive utilities