Research On Fuzzy Portfolio Optimization Problem Considering Short Selling

Modern portfolio deals with the problem of how to scientifically allocate investment proportion among different assets,so as to maximize the returns and minimize the risks.In actual portfolio management,short selling has become an important investment vehicle that attracts more and more investors' attention.Most of the fuzzy portfolio models are established without short selling,which cannot effectively guide investors to build reasonable portfolio strategies when short selling is allowed.Based on fuzzy set theory and portfolio theory,this thesis devotes itself to constructing a portfolio optimization model considering short selling under a fuzzy environment,in order to provide investors with more rational strategies in actual investment.The main research works of this thesis are listed as follows:(1)Construct a single period multi-objective fuzzy portfolio optimization model considering short selling.Based on the possibility theory,regard the return rates of risky assets as trapezoidal fuzzy numbers.With the objectives of maximizing the return and skewness,minimizing risk,kurtosis and fuzziness,and introducing constraints such as minimum trading lots constraint,bound constraint,and budget constraint,a single period multi-objective fuzzy portfolio optimization model considering short selling is established.Then,employ an improved multiple population genetic algorithm to solve the proposed model.Finally,give an example using real stock data to illustrate the feasibility and applicability of the proposed model and algorithm.(2)Construct a multi-period fuzzy portfolio optimization model considering short selling.Firstly,assume that the return rates of risky assets are trapezoidal fuzzy numbers,and measure the return and risk by credibilistic mean and credibilistic lower-semi-variance,respectively.Secondly,considering some realistic constraints such as single period return constraint,bankruptcy control constraint,bound constraint and budget constraint,establish a multi-period credibilistic mean-lower-semi-variance-skewness portfolio selection model with short selling,which aims at maximizing the terminal cumulative wealth and skewness,and minimizing the terminal cumulative risk.Then,design a modified multiple particle swarm optimization algorithm to solve the model.Finally,give a numerical example to illustrate the effectiveness of the proposed model and algorithm.(3)Construct a multi-period fuzzy portfolio optimization model considering several types of short selling constraints.To comprehensively consider the impact of short selling in the investment process,the model considers three types of short selling constraints,i.e.,total short selling proportion constraint,short selling cardinality constraint,and lower and upper bound constraint.Firstly,use trapezoidal fuzzy numbers to describe the returns of risky assets,and propose a multi-period possibilistic mean-semi-variance portfolio selection model with multiple short selling constraints.Secondly,design a multiple particle swarm optimization with simulated annealing to solve the proposed model.Finally,give an example to illustrate that the proposed model can help investors build an effective portfolio strategy when short selling is allowed,and the designed algorithm can effectively solve the proposed model and maintain good performance.This thesis rationally embeds short selling into the fuzzy portfolio optimization decisionmaking process and can guide investors to solve portfolio problems with short selling in the practical application.This enriches the theoretical implications for the modern portfolio theory and can provide a reference for actual investment.