Portfolio Optimization Under Criterion Of Maximizing:Geometric Average Expected Rate Of Return

With the sustainable development of China's economy,people's wealth is growing.The continuous improvement of China's capital market system and the continuous enrichment of investment channels have also facilitated the participation of ordinary investors in the capital market,which leads to the constant expansion of asset management by professional asset managers.How to manage investors' assets better and obtain higher returns for investors is an important issue for all asset management organizations,and also an important issue in academic research.This paper first introduces the existing research results on investment decision-making.The existing research results can be divided into two types.One is to explain the fluctuation rule of stock market by establishing mathematical model,and then to optimize the portfolio;the other is to use artificial intelligence related methods such as neural network,decision tree,etc.to establish the model to predict the future market performance,and then build the portfolio according to the forecast result.Then this paper introduces the classical investment theory,that is,Markowitz's mean variance investment theory and the capital asset pricing model based on it.Then,under the assumption that the stock closing price has homogeneous Markov,combined with the Markov correlation theory including irreducible,aperiodic,and Perron-Frobenius theorem,a general method for finding the product expectation limit of different time states of homogeneous Markov chain in finite state is deduced.That is,under certain conditions,the limit can be converted to the maximum eigenvalue problem of a particular matrix,making the problem easier to solve in practical applications.On the basis of this,we put forward the criterion of maximizing the geometric average expected return rate of portfolio optimization,and turn it into the problem of finding a portfolio that maximizes the maximum eigenvalue of a particular matrix related to the portfolio.Because this problem belongs to combinatorial optimization category,we introduce simulated annealing algorithm to solve it.Finally,according to the real transaction information of a-share market,we carry out empirical analysis.