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Theory And Computational Approaches For Portfolio Selection Model Under The Constraint Of Higher Moments

Posted on:2008-08-13Degree:MasterType:Thesis
Country:ChinaCandidate:Z J ChenFull Text:PDF
GTID:2189360212476257Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
In this thesis, Based on the Markowitz Mean-Variance model, the expectation is considered as one condition, the linear combination of the variance (the second central moment) and skewness (the third central moment) and kurtosis (the forth central moment) is regarded as objective function, so a portfolio selection model under the constraint of higher moments such as skewness and kurtosis is formed. Then using piecewise linear approaching method and substituting the population moment for the sample moment , we can solve it with the programming to realize the purpose of getting the portfolio optimization.The first chapter is mainly about the works done by before people and the conclusions they drawn.In the second chapter, a portfolio selection model under the constraint of higher moments without transaction cost and the linear approaching method are discussed. First, a portfolio selection model under the constraint of higher moments such as skewness and kurtosis is introduced. Then the existence of the solution to the model is proved. On this base, applying the Lagrange multiplier method, the equation that the analytic solution to the model satisfied is given. Since there is no explicit solution, considered of the actual needing, it is necessary to consider a linear approaching method of this problem. So using linear approaching method and substituting the population moment for the sample moment, the non-linear programming model is transferred approximately to a linear programming model. The solutions that obtained with this method not only satisfy the expectation of investor but also make the risk smaller and the skewness larger much and the kurtosis smaller probably. So the...
Keywords/Search Tags:skewness, kurtosis, higher moments, portfolio selection, linear programming, transaction costs
PDF Full Text Request
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