Jensen's Inequality for g-Convex Function under g-Expectation

Abstract

A real valued function defined on}$\mathbb{R}$ {\small is called}$g${\small --convex if it satisfies the following \textquotedblleft generalized Jensen's inequality\textquotedblright under a given}$g${\small -expectation, i.e., }$h({\mathbb{E}}^g[X])\le \mathbb{E}${\small, for all random variables}$X$ {\small such that both sides of the inequality are meaningful. In this paper we will give a necessary and sufficient conditions for a }$C^2${\small -function being}{\small -convex. We also studied some more general situations. We also studied}$g${\small -concave and}$g${\small -affine functions.

21 pages

References in corpus (1)

• Pricing, Hedging and Optimally Designing Derivatives Via Minimization of Risk Measures