Jensen's inequality for g-convex function under g-expectation

• 成果类型: Article
• 署名作者: Jia, Guangyan; Peng, Shige
• 署名单位: Shandong University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-009-0206-x
• 发表日期: 2010
• 页码: 217-239
• 关键词: nonlinear expectations; VISCOSITY SOLUTIONS; THEOREM

摘要

A real valued function h defined on R is called g-convex if it satisfies the generalized Jensen's inequality for a given g-expectation, i.e., h (E-g[X]) <= E-g [h (X)] holds for all random variables X such that both sides of the inequality are meaningful. In this paper we will give a necessary and sufficient condition for a C (2)-function being g-convex, and study some more general situations. We also study g-concave and g-affine functions, and a relation between g-convexity and backward stochastic viability property.