A Multi-Period Portfolio Optimization Model with Dynamic Risk Preference and Minimum Trading Constraint under Uncertainty
Keywords:
Portfolio Optimization, Multi‑Period Portfolio, Dynamic Risk Preference, Value at Risk (VaR), Minimum Trading Constraint, Genetic Algorithm, Uncertainty EnvironmentAbstract
The objective of this study was to develop a multi-period portfolio optimization model under uncertainty that simultaneously incorporates dynamic investor risk preference, Value at Risk (VaR), and minimum trading constraints to improve investment decision-making and risk management over a multi-period investment horizon. This study was an applied quantitative research based on mathematical modeling and portfolio optimization. The proposed model formulated asset returns within a multi-period uncertain environment, and the objective function was designed to maximize expected wealth while controlling risk through the VaR criterion. To reflect realistic investor behavior, risk preference was modeled dynamically across different time periods. In addition, a minimum trading constraint was incorporated to reduce transaction costs and avoid unnecessary portfolio reallocations. Real monthly financial data from ten major companies listed on the Tehran Stock Exchange during the period from 2018 to 2026 were extracted from the Rahavard 365 database. Due to the nonlinear and complex structure of the optimization model, a genetic algorithm was employed as the metaheuristic solution approach in MATLAB. The model performance was evaluated using sensitivity analysis and risk–return performance indicators. The findings demonstrated that the proposed model successfully established a balance between expected return and investment risk. The optimal portfolio achieved an expected return of 0.101 with a standard deviation of 0.187, while the VaR at the 95% confidence level was estimated at −0.208. Sensitivity analysis revealed that increasing the confidence level reduced portfolio risk while slightly decreasing expected return. Moreover, higher levels of risk aversion increased the allocation toward low-risk assets and reduced portfolio volatility. The results also indicated that relaxing the trading constraint improved expected return but increased portfolio turnover and risk exposure. Furthermore, the convergence behavior of the genetic algorithm confirmed that the algorithm effectively converged toward a stable and near-optimal solution. The results indicate that the proposed multi-period portfolio optimization model, by incorporating dynamic risk preference, VaR, and minimum trading constraints, provides an efficient and realistic framework for portfolio management under uncertainty. Additionally, the use of the genetic algorithm improved solution quality and enabled the identification of optimal investment allocations over a multi-period horizon.
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Copyright (c) 2025 Saber Bahraminejad (Author); Farid Asgari (Corresponding author); Ali Emami Meybodi, Babak Hajikarimi (Author)
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
