High Order Portfolio Optimization Problem with Transaction Costs

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.

The Digitalization Transformation of Commercial Banks and Its Impact on Sustainable Efficiency Improvements through Investment in Science and Technology

“…Most of the existing research on digital transformation explores regional and industrial level issues [13] and underscores the significant positive impact of the development of the Internet on upgrading the financial industry. At the firm level, research emphasizes tax burdens [14] from the perspective of external factors, including financing support [15]; other works focus on the labor flow from the perspective of internal factors and boosting the path of digitalization to transform enterprises [16].…”