A Multi-Period Optimization Framework for Portfolio Selection Using Interval Analysis

This paper presents a robust multi-period portfolio optimization framework that integrates interval analysis, entropy-based diversification, and downside risk control. In contrast to classical models relying on precise probabilistic assumptions, our approach captures uncertainty through interval-valued parameters for asset returns, risk, and liquidity-particularly suitable for volatile markets such as cryptocurrencies. The model seeks to maximize terminal portfolio wealth over a finite investment horizon while ensuring compliance with return, risk, liquidity, and diversification constraints at each rebalancing stage. Risk is modeled using semi-absolute deviation, which better reflects investor sensitivity to downside outcomes than variance-based measures, and diversification is promoted through Shannon entropy to prevent excessive concentration. A nonlinear multi-objective formulation ensures computational tractability while preserving decision realism. To illustrate the practical applicability of the proposed framework, a simulated case study is conducted on four major cryptocurrencies-Bitcoin (BTC), Ethereum (ETH), Solana (SOL), and Binance Coin (BNB). The model evaluates three strategic profiles based on investor risk attitude: pessimistic (lower return bounds and upper risk bounds), optimistic (upper return bounds and lower risk bounds), and mixed (average values). The resulting final terminal wealth intervals are [1085.32, 1163.77] for the pessimistic strategy, [1123.89, 1245.16] for the mixed strategy, and [1167.42, 1323.55] for the optimistic strategy. These results demonstrate the model's adaptability to different investor preferences and its empirical relevance in managing uncertainty under real-world volatility conditions.