This paper studies a high order moments portfolio optimization model with\ntransaction costs. The model takes kurtosis as objective function and takes the\nskewness, variance, mean and transaction costs as constraints conditions.\nSince the optimization problem is of high order and non-convex, it brings\nsome difficulties to the solution of the model. Therefore, this paper transforms\nthe optimization problem into a semi-definite matrix optimization\nproblem by using the moment matrix theory, and then solves it. Through the\nstudy of four risky assets in Chinaâ??s securities market, it is found that transaction\ncosts are significant parts in the study of portfolio model. In addition,\nsensitivity analysis shows that the kurtosis and skewness are positively correlated\nwith the mean and variance invariant. When mean and skewness are\nconstant, kurtosis and variance are positively correlated. When mean and\nskewness remain unchanged, the fourth order standard central moment and\nvariance are negatively correlated.
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