基于投资者动态损失厌恶模糊多目标投资组合问题研究

Research on Fuzzy Multi-objective Portfolio Modelwith Investors’Dynamic Loss Aversion

考虑投资者动态损失厌恶和证券市场的模糊不确定性,在可信性框架下以损失厌恶效用、流动性和下方风险为模糊多目标,构建考虑目标重要性的多阶段投资组合选择模型,提出TVSAPSO算法求解模型。以中国股市行业板块的实际数据为背景进行实证分析,研究发现,多阶段资产配置过程中,受动态损失厌恶特征影响,保守投资者倾向于关注流动性目标,偏好防御型行业和无风险资产,积极投资者倾向于关注损失厌恶效用目标,偏好风险型行业和防御型行业;积极投资者在最优期末财富方面的绩效表现优于保守投资者,保守投资者在风险调整后收益方面的绩效表现优于积极投资者。结果表明模糊多目标模型能够满足不同投资者的动态投资需求,为损失厌恶投资者进行多阶段资产配置和风险管理提供了有益的参考。

According to non-statistical uncertainty and insufficient historical data in security return forecasts,fuzzy set theory has been applied in the past decades to build portfolio selection models.This paper deals with a multi-objective portfolio selection problem in a fuzzy environment,in which the effects of investors’dynamic asymmetric attitudes to losses and gains on portfolio selection are considered.Due to different dynamic loss aversion characteristics,the portfolio performances of conservative and aggressive investors differ.In the fuzzy multi-objective portfolio model,it is necessary to consider investors’dynamic loss aversion characteristics.In multi-period asset allocation,loss-averse investors adjust their investment strategies dynamically.High liquidity assets are conducive to investors’timely adjustment of asset holdings and improvement of investment return.Because downside risk describes the volatility risk that investors bear when they suffer losses,loss-averse investors pay more attention to the portfolio’s downside risk.To meet the investment needs of dynamic loss-averse investors who pursue high portfolio liquidity and avoid downside risk,a credibilistic portfolio selection model is constructed with dynamic loss-averse utility,liquidity and downside risk as multi-objective,and the multi-stage investment decision-making problem of different types of investors affected by relative wealth changes is explored.Assuming that the return on assets and turnover rate are trapezoidal fuzzy numbers,the expected return,the lower semi-deviation and the expected liquidity of portfolios are derived,and a fuzzy multi-objective portfolio model is constructed under the credibilistic framework.The extended weighted Chebyshev programming method assigns different weights to each goal.The fuzzy multi-objective portfolio model is transformed into a single objective portfolio model,which allows conservative investors and aggressive investors to assign different importance to the investment target to meet the investment needs of various investors to weigh the difference of multi-objective time difference.A time-varying self-adaptive particle swarm optimization(TVSAPSO)is proposed to solve the model and add the time-varying inertia weight and acceleration coefficient to solve the problem of particle dynamic cognitive learningability and social learning ability in the stochastic ranking approach.The results show that the performance of the fuzzy multi-objective portfolio model considering dynamic loss aversion is better than that of the fuzzy multi-objective portfolio model considering static loss aversion and the mean-variance model.In the multi-period portfolio selection model,due to the different characteristics of dynamic loss aversion,there are differences in the importance of the objectives,asset structures,and the performance of the optimal portfolios of conservative and aggressive investors.Affected by the change in relative wealth,conservative investors are more sensitive to losses and prefer portfolios with higher liquidity levels to reduce the investment cost of adjusting portfolios.Conservative investors select the portfolio with the highest importance of liquidity,preferring defensive major consumer industry and risk-free assets.The risk-adjusted return of conservative investors’optimal portfolio is better than that of aggressive investors.Due to the existence of the break-even effect,aggressive investors pursue high returns to make up for early losses.Aggressive investors select the portfolio with the highest importance of loss aversion utility and prefer risky information and telecommunications industries and defensive major consumer industries.The results show that the fuzzy multi-objective model can meet the dynamic investment demands of different investors and provide a valuable reference for them to carry out multi-period asset allocation and risk management.This paper assumes that the loss aversion utility function is a piece-wise linear function.Furthermore,we will use the nonlinear function to describe the psychological characteristics of investors’different risk aversion to gain and loss.We also study the investment decision-making of dynamic loss aversion investors.