A refined Holder's inequality for Choquet expectation by Cauchy-Schwarz's inequality

摘要

In this paper, we first introduce a refined Holder's inequality in Choquet calculus. Then by this inequality, we show that Cauchy-Schwarz inequality and Wilder's inequality for Choquet expectation are equivalent when the monotone measure is submodular or the integrands are comonotonic, thus closing the series of papers in this literature. Note that it is obvious that Holder's inequality implies Cauchy-Schwarz's inequality. But the converse is an interesting subject. This paper focuses on this subject. (C) 2019 Elsevier Inc. All rights reserved.