| Financial market has systemic complexity and uncertainty.For investors,return and risk often coexist.How to reasonably allocate funds to different assets to obtain excess returns while well controlling risk,so as to maximize the return rate of the risk-adjusted portfolio is a problem worthy of continuous in-depth study.Portfolio optimization(PO)provides a useful attempt to achieve this goal,and some results have been achieved.Different from single objective PO model or simple multi-objective PO model,this paper systematically modeled several typical multi-objective portfolio optimization problems,and designed some efficient multi-objective swarm intelligence algorithms.By comparing with the comparison algorithms,the effectiveness of the designed algorithms to solve the models were verified.The main contents and innovations are as follows:(1)For single-stage multi-objective portfolio optimization problems.This paper first constructs a three-objective IRAROC-ES-E model.During the modeling process,key factors such as cost function,minimum income constraint,and investment ratio limit are considered,and the investment efficiency of the portfolio is measured by maximizing IRAROC.Entropy is used to reduce the tail risk faced by the investment portfolio.It also uses entropy to diversify the investment and avoid the concentration risk of the investment portfolio.Considering the excellent properties of the second-order differential evolution operator,the NSGA-II-SODE algorithm is designed by combining it with the NSGA-Ⅱ algorithm.Compared with the classic MOEA/D algorithm,NSGA-Ⅱ algorithm and NSGA-ⅡSDR algorithm,the newly designed NSGA-Ⅱ-SODE algorithm has advantages in terms of objective function and algorithm comprehensive performance evaluation index.In addition,considering the impact of liquidity on portfolio security,a multi-objective SNR-ES-TR model is constructed.At the same time,the model optimizes the investment efficiency,tail risk and liquidity level of the portfolio after the second half risk adjustment.The MOPSO framework is improved,and a MOPSO-SODE algorithm considering the second-order difference operator is designed.By comparing with MOEA/D algorithm,NSGA-Ⅱ-SDR algorithm,MOPSO algorithm and MOPSO-DE algorithm,the effectiveness of the designed MOPSO-SODE algorithm in solving SNR-ES-TR model is verified.(2)For a multi-stage multi-objective carbon-neutral stock portfolio optimization problem.This paper constructs a constrained M-ISTARRMD model that simultaneously optimizes the end-of-period value,tail riskadjusted investment efficiency,and drawdown of portfolio.In the process of constructing the model,constraints such as minimum income,liquidity,and dispersion are also taken into consideration.By introducing an orthogonal learning strategy,an efficient MSCMOEA-OL algorithm is designed and experimented on the constructed carbon-neutral stock portfolio asset pool.Compared with four classic constrained multi-objective solving algorithms such as NSGA-Ⅲ,ANSGA-Ⅲ,DCNAGA-Ⅲ and ARMOEA,the designed MSCMOEA-OL algorithm has a significant advantage in solving M-ISTARR-MD model.(3)For considering the multi-stage multi-objective portfolio optimization problem of mental account.This paper proposes a UM-USR-UTR model based on the mental account phenomenon,which takes into account uncertain risk,investment efficiency,liquidity and diversification.By extension and application of orthogonal learning strategy,DPCMOEA-OL algorithm based on double population evolution is designed.The method of factor analysis is used to construct the asset pool of the active investment mental account.The paper selects the"specialized,refinement,differential and innovation" concept stocks in A stock market,and realizes the combination of portfolio selection and portfolio optimization.By comparing with NSGA-Ⅲ,ANSGA-Ⅲ and DCNAGA-Ⅲ constrained multi-objective algorithms,the effectiveness of the proposed DPCMOEAOL algorithm in solving the UM-USR-UTR model based on two different types of mental accounts is verified. |
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