关键词: 动态损失厌恶, 可信性投资组合, 模糊多目标优化, TVSAPSO

Abstract: 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 portfoliÓs 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.

Key words: dynamic loss aversion, credibilistic portfolio, fuzzy multi-objective optimization, TVSAPSO