Research On Portfolio Selection Models With Background Risk Based On Multiple Measures

The essential problem of portfolio selection is how to disperse risk and make profit by constructing portfolios,which plays an important role in modern financial theory.The existing research only takes into account the uncertainty of financial markets when studies the risks that investors face.Although the risks in the non-financial market which are called background risk come from labor incomes,health status and real estate and so on,they change the mentality of investors and affect investors' decision-makings.If theoretical research just considers the risks that investors face in the financial market,and ignores the background risk in the non-financial market,the research conclusions may not conform the actual situations and lack of reliability and practicability.Therefore,investors should not only consider the risks that come from the financial market,but also consider the background risk that comes from non-financial market when research the portfolio selection problems.Based on this,this paper takes how to construct the portfolio selection models with background risk as the main research problem.The research of portfolio selection problem with background risk is a more comprehensive consideration of risks of investors,that is to say,it will play more comprehensive attention to the uncertainties on financial market and non-financial market.Then,how to measure the uncertainties has an important influence to the research conclusions.The uncertainty is mainly composed of random uncertainty,fuzzy uncertainty and mixed uncertainty.It is more comprehensive and systematic to study the portfolio selection problems with background risk under the three kinds of uncertainties and can make the research conclusions more robustness and reliability.Therefore,this paper uses multiple measures to carry out the research on the portfolio selection problems with background risk on the random uncertainty,fuzzy uncertainty and mixed uncertainty.The main research can be summarized as the following aspects:(1)We studied the portfolio selection problem with background risk based on the random uncertainty.Under the random uncertainty,considering the market was frictional,we first introduced the transaction cost into the construction of the model,and took the minimum risk and maximum return as the objectives to formulate a bi-objective meanvariance model with the background risk and transaction costs.Because it was difficult to get the analytical solution of the model,the improved genetic algorithm was proposed to solve the model and numerical examples were used to discuss the influence of the different preference degree of background risk and superiority of bi-objective mean-variance model with the background risk.Then,taking the CVaR risk measurement into mean-variance model,which satisfied the consistency condition,we proposed a bi-objective portfolio selection model with CVaR constraint.To illustrate the effect of CVaR,the comparison diagram of effective frontier of the two models was given.The result showed that the model with CVaR constraint controlled risks better and improved the returns of the portfolio.Finally,investors' sentiment was introduced into the bi-objective mean-variance model,and established the portfolio selection model with investors' sentiment and background risk by converting the two objectives to investors' maximized utility.Based on this,three theorems were proposed to illustrate the influence of investors' sentiment to the structure of financial assets and background risk.(2)We proposed the portfolio selection model with background risk under fuzzy uncertainty—established the fuzzy portfolio selection model with background risk under different business cycles.After constructing the portfolio selection models under random uncertainty,in view of the fuzziness is more profound and more widely in the real life than the randomness,this paper further studies the fuzzy portfolio selection models with background risk.First of all,using the knowledge of possibility theory and the assumption that the returns of assets were triangular fuzzy numbers,we constructed a fuzzy portfolio selection model with background risk under different business cycles about the investors who were risk aversion,used intelligent algorithm to solve the model and gave the portfolio,expectation variance and efficient frontiers under different business cycles.Then,considering the liquidity constraint affected the decision-makings on fuzzy uncertainty,we established a bi-objective portfolio selection model with liquidity constraint and background risk and obtain the optimal investment proportions.(3)We proposed the portfolio selection model with background risk under fuzzy uncertainty—proposed a fuzzy portfolio selection model with background risk under different attitudes.Based on the advantage of fuzzy uncertainty,we continue studying the portfolio selection model with background risk on fuzzy uncertainty.As investors were not limited to risk aversion by the influence of emotional attitudes,we defined the trapezoidal fuzzy numbers with risk attitudes,took the returns of assets were trapezoidal fuzzy numbers with risk attitudes and calculated the mean-variance model with background risk and different risk attitudes.Using the numerical examples,this paper analyzed effective frontier comparison chart of different risk attitudes.Based on the above model,we introduced the possibilistic entropy into it,and established the mean-variance-entropy model with background risk in the different attitudes.Finally,the two models were compared and analyzed by numerical examples.The result showed that the return per unit risk of mean-variance-entropy model was significantly higher than the mean-variance model.Therefore,we believed that the mean-variance-entropy model with background risk in the different attitudes was better than the mean-variance model with background risk.(4)We studied the portfolio selection model with background risk on mixed uncertainty.The uncertainty of the investors may face neither a pure random uncertainty,nor a pure fuzzy uncertainty,but the mixed uncertainty.Therefore,based on portfolio selection models with background risk on the random uncertainty and fuzzy uncertainty,we studied portfolio selection models with background risk on the mixture uncertainty.Fuzzy random measure is a combination of random measure and credibility measure.Therefore,we first introduced the credibility measure and established a portfolio selection model based on satisfaction with background risk and transaction costs.Then,combining the randomness and fuzziness,the fuzzy random measure was used to measure the mixed uncertainty.In this paper,the calculation formula of skewness was derived,and the multi-objective mean-variance-skewness model was established.By using the fuzzy programming,the model was transformed into a fuzzy random portfolio selection model with the satisfaction as the objective.At last,the relationship between satisfaction,background risk,portfolio return and variance was obtained.