Credibilistic mean-entropy models for multi-period portfolio selection with multi-choice aspiration levels

• We propose new multi-criteria credibilistic multi-period portfolio selection models.
• We use multiple aspiration levels using both the discrete choices and interval values.
• We use credibilistic entropy of the fuzzy returns to measure the portfolio risk.
• We include the liquidity, cardinality, and diversification constraints in the models.
• We use a fuzzy multi-choice goal programming method to obtain the trade-off solutions.

This paper deals with fuzzy multi-objective multi-period portfolio selection problems. The major criteria used for portfolio selection and rebalancing are wealth, risk, transaction cost, liquidity, and number of assets held in the portfolio. Considering that entropy as a measure of risk does not rely on any particular type of symmetric membership functions of the asset returns and can be computed from the nonmetric data as well, the portfolio risk is quantified using credibilistic entropy of the fuzzy returns. Furthermore, we use multi-choice aspiration levels for the financial goals to better suit the human perceptions such as “the more the better” or “the less the better” regarding return and risk. Two credibility-based fuzzy optimization models are developed using both the discrete choices and interval ranges for the multi-choice aspiration levels of each financial goal. To obtain efficient investment strategies for the entire investment horizon, we use a fuzzy credibilistic programming approach with multi-choice goal programming embedded in it. A real-world empirical application with data-set from an Indian stock market is presented to demonstrate usefulness of the proposed models and the solution approach for multi-period portfolio selection problem in fuzzy environment.