Jensen's Inequality for Generalized Peng's g -Expectations and Its Applications

Abstract

We study Jensen's inequality for generalized Peng's $g$-expectations and give four equivalent conditions on Jensen's inequality for generalized Peng's $g$-expectations without the assumption that the generator $g$ is continuous with respect to $t$. This result includes and extends some existing results. Furthermore, we give some applications of Jensen's inequality for generalized Peng's $g$-expectations.