Research On Portfolio Optimization Under Flexible Termination Time

Finance,as a medium of asset allocation,is becoming more and more significant with the rapid market's development and improvement.At the same time,people also pay more attention to the research of financial theory.The investment portfolio optimization is one of the most important researches of finance,which mainly studies how to allocate and select financial assets under uncertainty so as to balance the return and risk.All investors,including individual and institution,must face this problem.However,most of the past research mainly assumed that the investment deadline was fixed,which did not consider the investment time into the category of portfolio optimization.Actually,the investment opportunity is also an important factor of investment decision.Therefore,this thesis focuses on the portfolio optimization problem with flexible termination and study on that,this thesis presents the major work as follows:First of all,we summarize the modern portfolio theory and other related theories,such as risk management,through the collation and summary of relevant literature.On the basis of that,we characterize the portfolio problem with flexible deadline.Secondly,we establish a mathematical model of flexible deadline portfolio with mean absolute deviation,which is as the risk measurement,and then make simulation experiment under the Monte-Carlo simulation method.In order to facilitate solution,mathematical model is linearized.We use the CPLEX to make simulation experiments of five,ten and twenty stocks respectively under 1000 simulation conditions.In all,we make an analysis of the result.Finally,we establish a mathematical model of flexible deadline portfolio with value at risk,which is as the risk measurement,and then make simulation experiment under the Monte-Carlo simulation method.For ease of solution,it is transformed into a mixed integer programming model and solved by CPLEX.After testing,CPLEX can only solve the model under 500 simulations.Therefore,we design the Particle Swarm Optimization algorithm which base on the characteristics of Monte Carlo simulation model with value at risk.Iterated local search is embedded in the algorithm in order to jump out of the local best solution better.Then,we adjust the relevant parameters of PSO and compare the standard PSO with the PSO with iterated local search.We analyze the results under the best parameters.The results show that increasing the amount of stock investment can effectively reduce the risk;reducing the expected rate of return,the risk of the portfolio will also decrease.When the expected rate of return is reduced to a certain level,the risk reduction is no longer significant.Increasing the variable range of deadline time can reduce the risk as well,and as the time horizon increases to a certain level,the risk reduction is not significant.