Novel Fuzzy Portfolio Models Considering Minimax Expectations of Regret and Rejoice Based on Credibility Theory

Most scholars only consider regret value in financial decision-making, but pay little attention to the influence of ecstatic attitudes. However, in practice, both positive and negative feelings of investors affect their economic decisions. Based on this, two definitions of rejoice value are advanced. In one case, the rejoice value is defined as the distance between the minimum and the obtained return. In the other case, when the real return is greater than the return of equal weight portfolio, the rejoice value is measured by the distance between them. Corresponding to the above two definitions, we set the regret values respectively. Then, the regret aversion coefficient and rejoice coefficient are introduced, based on which, two regret–rejoice functions are defined by the linear weighting method. Moreover, two novel regret–rejoice expectation minimization fuzzy portfolio models are constructed by the above two new definitions. The security return is regarded as a fuzzy variable. Based on credibility theory, the corresponding regret–rejoice expectation is calculated by the fuzzy variable’s realization value and membership value. Finally, numerical examples based on China Shanghai Stock Exchange 180 Index are given to verify the effectiveness and practicality of our proposed models. Compared with the original model which considers only regret value, our novel regret–rejoice models have more efficient results in Sharpe ratio, monthly and weekly average logarithmic returns and cumulative logarithmic returns.