A Multi-Period Optimization Framework for Portfolio Selection Using Interval Analysis
Abstract
1. Introduction
2. Materials and Methods
2.1. Interval Analysis
2.2. Model Formulation
2.2.1. Notation
2.2.2. Objective and Constraints
2.2.3. The Multi-Period Portfolio Optimization Model with Interval Numbers
2.3. Solution Methodology
2.4. Case Study: Multi-Period Portfolio Selection Under Interval Uncertainty
- -
- Pessimistic: based on lower bounds for returns and upper bounds for risk.
- -
- Optimistic: using upper bounds for returns and lower bounds for risk.
- -
- Mixed: with average values between bounds, reflecting a neutral risk attitude.
3. Results and Discussion
- -
- Pessimistic: based on lower bounds for returns and upper bounds for risks;
- -
- Optimistic: using upper bounds for returns and lower bounds for risks;
- -
- Mixed: relying on the average of return and risk intervals, reflecting a balanced investor attitude.
- -
- Pessimistic: [1085.32, 1163.77]
- -
- Mixed: [1123.89, 1245.16]
- -
- Optimistic: [1167.42, 1323.55]
4. Conclusions
5. Future Research Directions
Funding
Data Availability Statement
Conflicts of Interest
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Asset | Return [t1] | Risk [t1] | Turnover [t1] | Return [t2] | Risk [t2] | Turnover [t2] | Return [t3] | Risk [t3] | Turnover [t3] |
---|---|---|---|---|---|---|---|---|---|
BTC | [0.03, 0.07] | [0.02, 0.05] | [0.1, 0.3] | [0.025, 0.065] | [0.018, 0.045] | [0.1, 0.25] | [0.02, 0.06] | [0.015, 0.04] | [0.1, 0.2] |
ETH | [0.025, 0.06] | [0.022, 0.048] | [0.08, 0.2] | [0.02, 0.055] | [0.02, 0.042] | [0.07, 0.18] | [0.015, 0.05] | [0.018, 0.038] | [0.07 0.16] |
SOL | [0.04, 0.08] | [0.03, 0.06] | [0.12, 0.28] | [0.035, 0.075] | [0.028, 0.055] | [0.1, 0.25] | [0.03, 0.07] | [0.025, 0.05] | [0.09, 0.22] |
BNB | [0.02, 0.05] | [0.015, 0.035] | [0.09, 0.2] | [0.018, 0.045] | [0.018, 0.045] | [0.013, 0.03] | [0.015, 0.04] | [0.01, 0.025] | [0.08, 0.15] |
Strategy | Terminal Wealth |
---|---|
Pessimistic | [1085.32, 1163.77] |
Mixed | [1123.89, 1245.16] |
Optimistic | [1167.42, 1323.55] |
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Șerban, F. A Multi-Period Optimization Framework for Portfolio Selection Using Interval Analysis. Mathematics 2025, 13, 1552. https://doi.org/10.3390/math13101552
Șerban F. A Multi-Period Optimization Framework for Portfolio Selection Using Interval Analysis. Mathematics. 2025; 13(10):1552. https://doi.org/10.3390/math13101552
Chicago/Turabian StyleȘerban, Florentin. 2025. "A Multi-Period Optimization Framework for Portfolio Selection Using Interval Analysis" Mathematics 13, no. 10: 1552. https://doi.org/10.3390/math13101552
APA StyleȘerban, F. (2025). A Multi-Period Optimization Framework for Portfolio Selection Using Interval Analysis. Mathematics, 13(10), 1552. https://doi.org/10.3390/math13101552