The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introductio...The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introduction,which gives a brief introduction to random metric theory,risk measures and conditional risk measures.Section 2 gives the central framework in random metric theory,topological structures,important examples,the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals.Section 3 gives several important representation theorems for random conjugate spaces.Section 4 gives characterizations for a complete random normed module to be random reflexive.Section 5 gives hyperplane separation theorems currently available in random locally convex modules.Section 6 gives the theory of random duality with respect to the locally L0-convex topology and in particular a characterization for a locally L0-convex module to be L0-pre-barreled.Section 7 gives some basic results on L0-convex analysis together with some applications to conditional risk measures.Finally,Section 8 is devoted to extensions of conditional convex risk measures,which shows that every representable L∞-type of conditional convex risk measure and every continuous Lp-type of convex conditional risk measure(1 ≤ p < +∞) can be extended to an L∞F(E)-type of σ,λ(L∞F(E),L1F(E))-lower semicontinuous conditional convex risk measure and an LpF(E)-type of T,λ-continuous conditional convex risk measure(1 ≤ p < +∞),respectively.展开更多
1. The Characteristics of land resources in Inner Mongolia1.1 The vast expance of land Accounting for 12.5 per cent of the Total area of China, the land area in InnerMongolia is 1.183 million square kilometer. The lan...1. The Characteristics of land resources in Inner Mongolia1.1 The vast expance of land Accounting for 12.5 per cent of the Total area of China, the land area in InnerMongolia is 1.183 million square kilometer. The land of per person in Inner Mongolia,which was 5.5 hectares, was 6.5 times of per person in China in 1990.展开更多
Taking the 12th Nanning Garden Expo as an example,this study analyzed its construction concept of "adjusting measures to local conditions and giving priority to protection".It is believed that the planning h...Taking the 12th Nanning Garden Expo as an example,this study analyzed its construction concept of "adjusting measures to local conditions and giving priority to protection".It is believed that the planning has preserved hills,rivers,ponds and other landforms as well as cultural relics to the greatest extent and protected the original landscape vegetation in the construction process.At the same time,through the ingenious layout of garden modeling,the plan integrated the concept of sponge city into the garden construction.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10871016)
文摘The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introduction,which gives a brief introduction to random metric theory,risk measures and conditional risk measures.Section 2 gives the central framework in random metric theory,topological structures,important examples,the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals.Section 3 gives several important representation theorems for random conjugate spaces.Section 4 gives characterizations for a complete random normed module to be random reflexive.Section 5 gives hyperplane separation theorems currently available in random locally convex modules.Section 6 gives the theory of random duality with respect to the locally L0-convex topology and in particular a characterization for a locally L0-convex module to be L0-pre-barreled.Section 7 gives some basic results on L0-convex analysis together with some applications to conditional risk measures.Finally,Section 8 is devoted to extensions of conditional convex risk measures,which shows that every representable L∞-type of conditional convex risk measure and every continuous Lp-type of convex conditional risk measure(1 ≤ p < +∞) can be extended to an L∞F(E)-type of σ,λ(L∞F(E),L1F(E))-lower semicontinuous conditional convex risk measure and an LpF(E)-type of T,λ-continuous conditional convex risk measure(1 ≤ p < +∞),respectively.
文摘1. The Characteristics of land resources in Inner Mongolia1.1 The vast expance of land Accounting for 12.5 per cent of the Total area of China, the land area in InnerMongolia is 1.183 million square kilometer. The land of per person in Inner Mongolia,which was 5.5 hectares, was 6.5 times of per person in China in 1990.
文摘Taking the 12th Nanning Garden Expo as an example,this study analyzed its construction concept of "adjusting measures to local conditions and giving priority to protection".It is believed that the planning has preserved hills,rivers,ponds and other landforms as well as cultural relics to the greatest extent and protected the original landscape vegetation in the construction process.At the same time,through the ingenious layout of garden modeling,the plan integrated the concept of sponge city into the garden construction.
