A multi-period fuzzy portfolio optimization model with investors' loss aversion

This paper considers the problem of how to construct the optimal multi-period portfolio for investors with loss aversion in fuzzy environment. Firstly, we regard the return rates of the risky assets as fuzzy numbers and use the value function in prospect theory to transform the return rate of a portfolio into perceived value, which can reflect investors' loss aversion. Moreover, due to the fact that investors' perception level toward risk may vary with the loss aversion degree, we propose a new risk measure based on the perceived value. Then, we formulate the objectives of maximizing the cumulative expected perceived value and minimizing the cumulative perceived risk and propose a multi-period portfolio selection model with diversification constraint. Furthermore, to solve the proposed model, we design a multiple particle swarm optimization algorithm with respect to its specific situation. Finally, using the data from real financial market, we construct a real case to illustrate the effectiveness of the model and algorithm. The results show that loss aversion has an important effect on investors' investment decisions, and the proposed model could provide more reasonable strategies for investors with different loss aversion degrees.

Automated summary

This paper discusses the problem of constructing the optimal multi-period portfolio for loss-averse investors in a fuzzy environment. The return rates of risky assets are considered as fuzzy numbers, and a value function based on prospect theory is used to transform the return rate into perceived value, reflecting investors' loss aversion. A new risk measure based on perceived value is proposed to account for varying risk perception levels with different degrees of loss aversion. The objectives of maximizing cumulative expected perceived value and minimizing cumulative perceived risk are formulated, and a multi-period portfolio selection model with diversification constraint is proposed. A multiple particle swarm optimization algorithm is designed to solve the model. A real case using data from the financial market is constructed to illustrate the effectiveness of the model and algorithm, showing that the proposed model can provide more reasonable strategies for investors with different degrees of loss aversion.