A Multiperiod Optimization Framework for Portfolio Selection Using Interval Analysis

This paper presents a comprehensive multi-period portfolio optimization framework that leverages interval analysis, entropy-based diversification, and downside risk con-trol to address uncertainty in financial decision-making. Unlike traditional models that rely on point estimates and precise probability distributions, the proposed approach captures the inherent imprecision of emerging or highly volatile markets by repre-senting asset returns, risks, and liquidity as interval-valued parameters. This interval representation enhances model realism and flexibility, especially when reliable histor-ical data is sparse or market conditions fluctuate unpredictably. The optimization ob-jective is to maximize terminal portfolio wealth over a discrete investment horizon, while simultaneously ensuring that performance constraints—related to return, risk, liquidity, and diversification—are satisfied at each rebalancing period. Risk is modeled using the semi-absolute deviation measure, which better reflects investors' aversion to downside losses compared to traditional variance-based approaches. Diversification is promoted via a proportion entropy function that penalizes overly concentrated asset allocations, fostering robustness in uncertain environments. The overall problem is formulated as a multi-objective fuzzy programming model with interval coefficients, which is then transformed into a crisp nonlinear optimization problem to enable trac-table numerical implementation. We validate the model through a simulated case study involving cryptocurrencies. The results highlight the model's adaptability to various investor profiles by comparing three strategic perspectives: pessimistic, opti-mistic, and mixed. The proposed framework offers a robust, versatile, and computa-tionally efficient tool for portfolio managers aiming to navigate uncertainty and opti-mize performance across multiple financial dimensions. It bridges the gap between theoretical modeling and practical asset management in uncertain market condition.