Weighted G-Expectation And Related Properties

This paper mainly studies on some problems of weighted g-expectation.In chapter 1,we introduce some backgrounds and research status and main contents.The basic concepts and related properties of g-expectation are also briefly introduced,which provide theoretical knowledge for research.In chapter 2,we research subadditivity and monotonicity on ? for weighted g-expectation,which is defined on the notation of g-expectation.We also study the relationship between Choquet expectation and weighted g-expectation,and we find that weighted g-expectation can be controlled by Choquet expectation which is induced by weighted g-expectation.We discover some inequalities of weighted g-expectation,as well.In chapter 3,We investigate the properties of weighted g-probability,weighted g-variance and weighted g-covariance,and relationships between weighted g-probability,weighted g-variance and weighted g-covarince.Meanwhile,the relationships between weighted g-variance,weighted g-expectation are showed.