In this paper, from the viewpoint of the time value of money, we study the risk measures for portfolio vectors with discount factor. Cash subadditive risk measures for portfolio vectors are proposed. Representation re...In this paper, from the viewpoint of the time value of money, we study the risk measures for portfolio vectors with discount factor. Cash subadditive risk measures for portfolio vectors are proposed. Representation results are given by two different methods which are convex analysis and enlarging space. Especially, the method of convex analysis make the line of reasoning and the representation result be simpler. Meanwhile, spot and forward risk measures for portfolio vectors are also introduced, and the relationships between them are investigated.展开更多
In this paper, new risk measures are introduced, tation results are also given. These newly introduced risk introduced by Song and Yan （2009） and Karoui （2009）. and the corresponding represen- measures are extens...In this paper, new risk measures are introduced, tation results are also given. These newly introduced risk introduced by Song and Yan （2009） and Karoui （2009）. and the corresponding represen- measures are extensions of those展开更多
In this paper, by an axiomatic approach, we propose the concepts of comonotonic subadditivity and comonotonic convex risk measures for portfolios, which are extensions of the ones introduced by Song and Yan （2006）. ...In this paper, by an axiomatic approach, we propose the concepts of comonotonic subadditivity and comonotonic convex risk measures for portfolios, which are extensions of the ones introduced by Song and Yan （2006）. Representation results for these new introduced risk measures for portfolios are given in terms of Choquet integrals. Links of these newly introduced risk measures to multi-period comonotonic risk measures are represented. Finally, applications of the newly introduced comonotonic coherent risk measures to capital allocations are provided.展开更多
Two types of uncertainty co-exist in the theory of evidence： discord and non-specificity.From 90s, many mathematical expressions have arisen to quantify these two parts in an evidence.An important aspect of each meas...Two types of uncertainty co-exist in the theory of evidence： discord and non-specificity.From 90s, many mathematical expressions have arisen to quantify these two parts in an evidence.An important aspect of each measure presented is the verification of a coherent set of properties.About non-specificity, so far only one measure verifies an important set of those properties. Very recently, a new measure of non-specificity based on belief intervals has been presented as an alternative measure that quantifies a similar set of properties（Yang et al., 2016）. It is shown that the new measure really does not verify two of those important properties. Some errors have been found in their corresponding proofs in the original publication.展开更多
Two theorems are proved. They are with principal significance in functional analysis, for they imply some well known theorems, such as the open mapping theorem, the closed graph theorem and the Banach Steinhaus theo...Two theorems are proved. They are with principal significance in functional analysis, for they imply some well known theorems, such as the open mapping theorem, the closed graph theorem and the Banach Steinhaus theorem.展开更多
基金Supported by the National Natural Science Foundation of China(11371284,11771343)
文摘In this paper, from the viewpoint of the time value of money, we study the risk measures for portfolio vectors with discount factor. Cash subadditive risk measures for portfolio vectors are proposed. Representation results are given by two different methods which are convex analysis and enlarging space. Especially, the method of convex analysis make the line of reasoning and the representation result be simpler. Meanwhile, spot and forward risk measures for portfolio vectors are also introduced, and the relationships between them are investigated.
基金Supported in part by the National Natural Science Foundation of China (10971157)Key Projects of Philosophy and Social Sciences Research+1 种基金Ministry of Education of China (09JZD0027)The Talent Introduction Projects of Nanjing Audit University
文摘In this paper, new risk measures are introduced, tation results are also given. These newly introduced risk introduced by Song and Yan （2009） and Karoui （2009）. and the corresponding represen- measures are extensions of those
基金Supported by the National Natural Science Foundation of China(11371284)the Natural Science Foundation of Henan Province(14B110037)
文摘In this paper, by an axiomatic approach, we propose the concepts of comonotonic subadditivity and comonotonic convex risk measures for portfolios, which are extensions of the ones introduced by Song and Yan （2006）. Representation results for these new introduced risk measures for portfolios are given in terms of Choquet integrals. Links of these newly introduced risk measures to multi-period comonotonic risk measures are represented. Finally, applications of the newly introduced comonotonic coherent risk measures to capital allocations are provided.
基金supported by the Spanish ‘‘Ministerio de Economíay Competitividad"by ‘‘Fondo Europeo de Desarrollo Regional"(FEDER)(No.TEC2015-69496-R)
文摘Two types of uncertainty co-exist in the theory of evidence： discord and non-specificity.From 90s, many mathematical expressions have arisen to quantify these two parts in an evidence.An important aspect of each measure presented is the verification of a coherent set of properties.About non-specificity, so far only one measure verifies an important set of those properties. Very recently, a new measure of non-specificity based on belief intervals has been presented as an alternative measure that quantifies a similar set of properties（Yang et al., 2016）. It is shown that the new measure really does not verify two of those important properties. Some errors have been found in their corresponding proofs in the original publication.
文摘Two theorems are proved. They are with principal significance in functional analysis, for they imply some well known theorems, such as the open mapping theorem, the closed graph theorem and the Banach Steinhaus theorem.
