In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational ineq...In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree meth- od of acute angle principle about monotone operator as an application of these results.展开更多
In this paper,we give an overview of representation theorems for various static risk measures:coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity, law-invariant coherent or conv...In this paper,we give an overview of representation theorems for various static risk measures:coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity, law-invariant coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity and respecting stochastic orders.展开更多
文摘In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree meth- od of acute angle principle about monotone operator as an application of these results.
基金supported by National Natural Science Foundation of China (Grant No.10571167)National Basic Research Program of China (973 Program) (Grant No.2007CB814902)Science Fund for Creative Research Groups (Grant No.10721101)
文摘In this paper,we give an overview of representation theorems for various static risk measures:coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity, law-invariant coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity and respecting stochastic orders.
