Based On The Credibility Of Higher Order Moment With Different Entropy Research Of Portfolio Model

Portfolio selection of Markowitz is a cornerstone of modern finance theory,its application is very broad,including the field of finance,financial engineering,financial mathematics and so on.The events tend to have double properties in securities markets,it is randomness and fuzziness.There are many research achievements of portfolio problems under the random environment.Therefore research of portfolio problems has certain significance under the fuzzy environment.In this paper,we discuss portfolio problems with different entropy based on credibility theory that put forward by Liu Baoding professor,the paper's main contents are as follows:(1)In the classic mean-variance model,the researchers tend to assume that yields obey normal distribution,but yields often does not meet the assumption in the fact,and considering the limitations of variance.So we build mean-entropy model,average yields can be calculated by each time period yields and product yields weight to the total time period,and measure risk by entropy,then comparing with mean-variance model,we found entropy has quite diversification.(2)Considering the Shannon entropy and Yager entropy has some shortcomings,Shannon entropy due to the properties of the logarithmic function,causing the portfolio model of low diversity,making assets return cannot achieve the expected return;And also due to the extreme value properties of Yager entropy,only when the weight coefficient are equals,it can get maximum entropy.Therefore considering the properties of these two kinds of entropy,we can construct a new entropy based on the Malinowski distance formula,then we build the mean-Yager entropy model and mean-proportion entropy model,through the empirical analysis found that the proportion entropy can be very good to avoid the defect of Shannon entropy and Yager entropy,the diversity of its model of solution is good.(3)Because of the new parameter that is contained in the proportion of entropy,considering whether parameters effect on the portfolio model solution;Also because of the asymmetry of the asset return,we can construct portfolio model of higher order moment based on credibility theory,which estimate assets return by the mean of credibility measure,estimate risk by credibility absolute measure of the second half,estimate the diversity of the portfolio by proportion entropy,also estimate the asymmetry of assets by partial degree;In order to make the portfolio model more accord with the actual securities market,then considering transaction costs,liquidity conditions and so on;Finally using particle swarm optimization algorithm,we found that there are not great affection when the parameter ofproportion of entropy has changed.In a word,we build higher order moment with different entropy of portfolio model based on the credibility theory under fuzzy environment,this study enriches the research of portfolio under fuzzy environment,also has important theoretical and practical significance.