Research On Fuzzy Portfolio Optimization Problem Considering Transaction Costs

Portfolio theory is one of the core areas of modern financial research,portfolio theory is the study of investors in a variety of assets in order to maximize the allocation of income or minimize risk.Due to the impact of investor psychological activities and various policy restrictions,so in constructing the portfolio to consider the linkage effect of friction between market discipline and various assets,and thus to build a portfolio to increase the difficulty,so more than half a century,many scholars have made a breakthrough and development of portfolio theory of Markowitz from different angles.As the investment itself is a matter of uncertainty,and the result is also a matter of uncertainty,which constitutes a fuzzy matter.With the birth of fuzzy mathematics,many economists began to apply fuzzy mathematics to the problem of portfolio decision making.When investors make investment decisions,the liquidity of securities is often an important factor for investors to consider.In the process of investment,every time the investor changes the transaction,there will be a certain cost,which will lead to an increase in transaction costs,which will increase the cost of investors,and then affect the effective frontier of investors.Due to the liquidity of securities related to the subjective intention and the stock market investors the maturity of uncertainty,while the securities investors concerned about the degree of mobility is an uncertain matter,so it can be regarded as a fuzzy matter for processing.In this paper,from the perspective of fuzzy uncertainty,the return and CVaR risk function are taken as the optimization target under the premise of considering the fuzzy liquidity constraint,establish a mean-CVaR portfolio model fuzzy liquidity constraints with transaction costs.And through the selection of the SSE 50 Index constituent stocks in the sample stock by numerical an example.Compare the impact of different transaction costs on investment under the constraints of liquidity and CVaR,so as to provide some reference for investors who take VaR or CVaR value as the risk measurement index.