Fuzzy portfolio selection with prospect consistency constraint based on possibility theory

Abstract

Considering that most studies have taken the investors’ preference for risk into account but ignored the investors’ preference for assets, in this paper, we combine the prospect theory and possibility theory to provide investors with a portfolio strategy that meets investors’ preference for assets. Firstly, a novel reference point is proposed to give investors a comprehensive impression of assets. Secondly, the prospect return rate of assets is quantified as trapezoidal fuzzy number, and its possibilistic mean value and variance are regarded as prospect return and risk and then used to define the fuzzy prospect value. This new definition is presented to denote the score of an asset in investors’ subjective cognition. And then, a prospect asset filtering frame is proposed to help investors select assets according to their preference. When assets are selected, another new definition called prospect consistency coefficient is proposed to measure the deviation of a portfolio strategy from investors’ preference. Some properties of the definition are presented by rigorous mathematical proof. Based on the definition and its properties, a possibilistic model is constructed, which can not only provide investors optimal strategies to make profit and reduce risk as much as possible, but also ensure that the deviation between the strategies and investors’ preference is tolerable. Finally, a numerical example is given to validate the proposed method, and the sensitivity analysis of parameters in prospect value function and prospect consistency constraint is conducted to help investors choose appropriate values according to their preferences. The results show that compared with the general M-V model, our model can not only better satisfy investors’ preference for assets, but also disperse risk effectively.