Decision-making of investors at the stock exchange can be based on the fundamental indicators of stocks, on the technical indicators, or can exist as a combination of these two methods. The paper gives emphasis to the...Decision-making of investors at the stock exchange can be based on the fundamental indicators of stocks, on the technical indicators, or can exist as a combination of these two methods. The paper gives emphasis to the domain of technical analysis. In the broader sense the technical analysis enables the dynamics of the expected future values of the shares estimation. This can be performed on the basis of the data on historical trends of the revenues, profits and other indicators from the balance sheet, but also on the basis of historical data on changes in the values of the shares. Companies generally belong to the different sectors that have different presumptions of development resulting from the global market trends, technology and other characteristic. Processing of historical data values of the outstanding shares of the Zagreb Stock Exchange （ZSE） is origination of this research. Investors are interested to know the estimation of future returns for the stocks as well as the size of the risk associated with the expected returns. Research task in this paper is finding the optimal portfolio at the ZSE based on the concept of dominant portfolio by Markowitz approach. The portfolio is created by solving non-linear programming problem using the common software tools. The results of obtained optimal portfolios contain relevant conclusions about the specifics of the shares as well as the characteristics of the industrial sectors but also provide a further knowledge about diverse sectors treatment at the stock exchange in a multi-year period.展开更多
We consider the design of semidefinite programming （SDP） based approximation algorithm for the problem Max Hypergraph Cut with Limited Unbalance （MHC-LU）： Find a partition of the vertices of a weighted hypergraph...We consider the design of semidefinite programming （SDP） based approximation algorithm for the problem Max Hypergraph Cut with Limited Unbalance （MHC-LU）： Find a partition of the vertices of a weighted hypergraph H = （V, E） into two subsets V1, V2 with ｜｜V2｜ - ｜1/1 ｜｜ ≤ u for some given u and maximizing the total weight of the edges meeting both V1 and V2. The problem MHC-LU generalizes several other combinatorial optimization problems including Max Cut, Max Cut with Limited Unbalance （MC-LU）, Max Set Splitting, Max Ek-Set Splitting and Max Hypergraph Bisection. By generalizing several earlier ideas, we present an SDP randomized approximation algorithm for MHC-LU with guaranteed worst-case performance ratios for various unbalance parameters τ = u/｜V｜. We also give the worst-case performance ratio of the SDP-algorithm for approximating MHC-LU regardless of the value of τ. Our strengthened SDP relaxation and rounding method improve a result of Ageev and Sviridenko （2000） on Max Hypergraph Bisection （MHC-LU with u = 0）, and results of Andersson and Engebretsen （1999）, Gaur and Krishnamurti （2001） and Zhang et al. （2004） on Max Set Splitting （MHC-LU with u = ｜V｜）. Furthermore, our new formula for the performance ratio by a tighter analysis compared with that in Galbiati and Maffioli （2007） is responsible for the improvement of a result of Galbiati and Maffioli （2007） on MC-LU for some range of τ.展开更多
Seawater intrusion problem is considered in this paper.Its mathematical model is anonlinear coupled system of partial differential equations with initial boundary problem.It consistsof the water head equation and the ...Seawater intrusion problem is considered in this paper.Its mathematical model is anonlinear coupled system of partial differential equations with initial boundary problem.It consistsof the water head equation and the salt concentration equation.A combined method is developedto approximate the water head equation by mixed finite element method and concentration equationby discontinuous Galerkin method.The scheme is continuous in time and optimal order estimates inH^1-norm and L^2-norm are derived for the errors.展开更多
文摘Decision-making of investors at the stock exchange can be based on the fundamental indicators of stocks, on the technical indicators, or can exist as a combination of these two methods. The paper gives emphasis to the domain of technical analysis. In the broader sense the technical analysis enables the dynamics of the expected future values of the shares estimation. This can be performed on the basis of the data on historical trends of the revenues, profits and other indicators from the balance sheet, but also on the basis of historical data on changes in the values of the shares. Companies generally belong to the different sectors that have different presumptions of development resulting from the global market trends, technology and other characteristic. Processing of historical data values of the outstanding shares of the Zagreb Stock Exchange （ZSE） is origination of this research. Investors are interested to know the estimation of future returns for the stocks as well as the size of the risk associated with the expected returns. Research task in this paper is finding the optimal portfolio at the ZSE based on the concept of dominant portfolio by Markowitz approach. The portfolio is created by solving non-linear programming problem using the common software tools. The results of obtained optimal portfolios contain relevant conclusions about the specifics of the shares as well as the characteristics of the industrial sectors but also provide a further knowledge about diverse sectors treatment at the stock exchange in a multi-year period.
基金supported by National Natural Science Foundation of China(Grant Nos.11171160,11331003 and 11471003)the Priority Academic Program Development of Jiangsu Higher Education Institutions+2 种基金the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.13KJB1100188)Natural Science Foundation of Guangdong Province(Grant No.S2012040007521)Sienceand Technology Planning Project in Guangzhou(Grant No.2013J4100077)
文摘We consider the design of semidefinite programming （SDP） based approximation algorithm for the problem Max Hypergraph Cut with Limited Unbalance （MHC-LU）： Find a partition of the vertices of a weighted hypergraph H = （V, E） into two subsets V1, V2 with ｜｜V2｜ - ｜1/1 ｜｜ ≤ u for some given u and maximizing the total weight of the edges meeting both V1 and V2. The problem MHC-LU generalizes several other combinatorial optimization problems including Max Cut, Max Cut with Limited Unbalance （MC-LU）, Max Set Splitting, Max Ek-Set Splitting and Max Hypergraph Bisection. By generalizing several earlier ideas, we present an SDP randomized approximation algorithm for MHC-LU with guaranteed worst-case performance ratios for various unbalance parameters τ = u/｜V｜. We also give the worst-case performance ratio of the SDP-algorithm for approximating MHC-LU regardless of the value of τ. Our strengthened SDP relaxation and rounding method improve a result of Ageev and Sviridenko （2000） on Max Hypergraph Bisection （MHC-LU with u = 0）, and results of Andersson and Engebretsen （1999）, Gaur and Krishnamurti （2001） and Zhang et al. （2004） on Max Set Splitting （MHC-LU with u = ｜V｜）. Furthermore, our new formula for the performance ratio by a tighter analysis compared with that in Galbiati and Maffioli （2007） is responsible for the improvement of a result of Galbiati and Maffioli （2007） on MC-LU for some range of τ.
基金supported by the National Natural Science Foundation of China under Grant No. 10771124
文摘Seawater intrusion problem is considered in this paper.Its mathematical model is anonlinear coupled system of partial differential equations with initial boundary problem.It consistsof the water head equation and the salt concentration equation.A combined method is developedto approximate the water head equation by mixed finite element method and concentration equationby discontinuous Galerkin method.The scheme is continuous in time and optimal order estimates inH^1-norm and L^2-norm are derived for the errors.
