TITLE:
High Order Portfolio Optimization Problem with Transaction Costs
AUTHORS:
Xin Li, Peiai Zhang
KEYWORDS:
Portfolio, High Order Moment, Transaction Costs, Sensitivity Analysis
JOURNAL NAME:
Modern Economy,
Vol.10 No.6,
June
12,
2019
ABSTRACT: This paper studies a high order moments portfolio
optimization model with transaction costs. The model takes kurtosis as
objective function and takes the skewness, variance, mean and transaction costs
as constraints conditions. Since the optimization problem is of high order and
non-convex, it brings some difficulties to the solution of the model.
Therefore, this paper transforms the optimization problem into a semi-definite
matrix optimization problem by using the moment matrix theory, and then solves
it. Through the study of four risky assets in China’s securities market, it is
found that transaction costs are significant parts in the study of portfolio
model. In addition, sensitivity analysis shows that the kurtosis and skewness
are positively correlated with the mean and variance invariant. When mean and
skewness are constant, kurtosis and variance are positively correlated. When
mean and skewness remain unchanged, the fourth order standard central moment
and variance are negatively correlated.