Quadratic gg-convexity, CC-convexity and their relationships

In this paper we study Jensen’s inequality under quadratic gg-expectation, i.e., the expectation generated by backward stochastic differential equations (BSDEs) with generator of quadratic growth in its component zz. In particular, we define a new kind of convexity, the CC-convexity, via a second order ODE depending on a real constant CC, and we study the relationships between quadratic gg-convexity and CC-convexity.