Backward Nonlinear Expectation Equations
Mathematics and Financial Economics, Vol. 12, No. 1, pp. 111-134, 2018
Posted: 11 Jan 2015 Last revised: 10 Jan 2019
Date Written: August 1, 2017
Abstract
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.
Keywords: backward stochastic differential equation, nonlinear expectation, random G-expectation, recursive utility, volatility uncertainty
JEL Classification: D81, D91
Suggested Citation: Suggested Citation