Moment Inequality and Holder Inequality for BSDEs

Under the Lipschitz and square integrable assumptions on the generator g of BSDEs, this paper proves that if g is positively homogeneous in (y, z) and is decreasing in y, then the Moment inequality for BSDEs with generator g holds in general, and if g is positively homogeneous and sub-additive in (y, z), then the Holder inequality and Minkowski inequality for BSDEs with generator g hold in general.