Jensen's Inequality for Backward SDEs Driven by $G$-Brownian motion

Abstract

In this note, we consider Jensen's inequality for the nonlinear expectation associated with backward SDEs driven by $G$-Brownian motion ($G$-BSDEs for short). At first, we give a necessary and sufficient condition for $G$-BSDEs under which one-dimensional Jensen inequality holds. Second, we prove that for $n>1$, the $n$-dimensional Jensen inequality holds for any nonlinear expectation if and only if the nonlinear expectation is linear, which is essentially due to Jia (Arch. Math. 94 (2010), 489-499). As a consequence, we give a necessary and sufficient condition for $G$-BSDEs under which the $n$-dimensional Jensen inequality holds.

11 pages

References in corpus (2)

• A New Central Limit Theorem under Sublinear Expectations
• Comparison Theorem, Feynman-Kac Formula and Girsanov Transformation for BSDEs Driven by G-Brownian Motion