Uncertain Portfolio Model Considering Transaction Costs Under Optimistic Value Criterion

With the rapid development of the financial market,a large number of investors invest their capital in the financial market to obtain excess returns.People construct portfolios to invest capital in different risky securities to diversify a market volatility risk in order to achieve a relative maximum return.Therefore,getting an optimal asset allocation decision is of great significance.Since Markowitz put forward the mean-variance model to quantify the risk and return of investment,many researchers have constructed more portfolio models based on the mean-variance model to make the models more suitable for market conditions and obtain better investment decisions.However,most of the past studies were considered based on random situations,in the real financial market,the historical data could not reflect the future due to the information incompleteness,policy uncertainty and emergencies.Based on the uncertainty theory,this paper considers the single period and continuous time and constructs two kinds of uncertain portfolio models which are close to the actual situation of the financial market.Firstly,this paper studies a one-stage uncertain portfolio model based on realistic constraints is studied.In order to better match investors’ preferences,realistic constraints such as transaction cost and liquidity demand are taken into account in the model.As VaR is defined as an optimistic estimate of loss,CVaR overcomes some defects of VaR.This paper uses CVaR as a measure of portfolio risk and turnover rate to describe the liquidity of securities.Due to the uncertainty and lack of relevant data in the future,both renturn rate and turnover rate are considered to be uncertain variables.Then,we design a genetic algorithm to solve the problem.Finally,this paper gives a numerical experiment as an illustration.Then,this paper studies the optimal investment decision of defined-contribution pension in continuous time.Taking inflation and transaction costs into account,the model sets the target payout and the target stock investment amount to construct the quadratic loss function as the objective function,and the fund managers put their wealth into different assets to minimize the present value of the quadratic loss function.The optimal control model of DC pension plan is established by using optimal control method under the uncertain optimistic value criterion.Using optimality principle and equation of optimality to solve the proposed problems to obtain the optimal pension investment strategy.Finally,a numerical experiment is presented as the validity of the model.