Optimization Of Investment Portfolio Based On Kernel Principal Component Analysis And Improved Mean-entropy Model

The financial market is complex.Investors are trying to pursue high returns and low risks in the process of capital market investment.Here we are committed to optimizing the investment portfolio from the perspective of risk diversification.Attilio Meucci(2010)uses entropy to define a degree of decentralization index in his literature.Among them,the combination configuration ratio is adjusted by principal component analysis(PCA).Principal component analysis is a linear analysis method,but non-linearity is common in financial markets,so its model lacks applicability in actual financial practice,and it is insufficient to describe non-linearity.This article is based on the basic portfolio model,uses semi-variance to measures the risk of the portfolio,following the risk diversification method of ??Attilio Meucci(2010).And we improve the algorithm.In this essay,we adjust the portfolio allocation ratio,take entropy as the standard risk diversification level,and use this indicator as the objective function of the portfolio to construct a mean-entropy model to achieve portfolio risk diversification.The model constructed in this article is suitable for long and short trading markets.Based on the improved model,we use stocks of CSI 300 Index here to do empirical analysis,based on a rolling time window.And external sample data are used to evaluate the performance of the portfolio.Based on the classic theory,this paper improves the Attilio Meucci's model algorithm,adjusts the nominal weight of assets through kernal principal component analysis,and uses the maximum entropy index to measure the level of risk diversification,further realize the diversification of investment portfolio risk.So as to avoid excessive concentration of risks of a certain investment target.At the same time,combined with practice,it is forward-looking at the level of model construction and empirical analysis.