Some important inequalities for g-expectation and Choquet expectation

摘要

In this paper, several important inequalities for g-expectation and Choquet expectation are obtained by using back-ward stochastic differential equations (BSDEs) and comparison theorem. Markov inequality for g-probability is a special case of this inequality. If the generator g is independent on y and is linear in z, some classical inequalities for Choquet capacity are also presented.