A generalized stochastic differential utility driven by G-Brownian motion

This paper introduces a class of generalized stochastic differential utility (GSDU) models in a continuous-time framework to capture ambiguity aversion on the financial market. This class of GSDU models encompasses several classical approaches to ambiguity aversion and includes new models about ambiguity aversion. For a general GSDU model, we demonstrate its continuity, monotonicity, time consistency, concavity, and homotheticity. We investigate its comparative ambiguity aversion and direction aversion under sufficient conditions. We further solve an optimal portfolio choice problem in one GSDU model as an application.