A new approach for multi-stage portfolio optimization under uncertainty conditions using scenario trees an‎d considering short selling

10/5/2026 12:00:00 AM

Investing in financial markets is inherently subject to various uncertainties an‎d dynamic market complexities. In this research, a novel approach for multi-stage portfolio optimization under uncertainty is proposed, utilizing a scenario tree framework while considering short selling. To model uncertainty, the weekly returns of selec‎ted stocks from the NASDAQ index over the past year were extracted. By sorting these returns, the average of the lowest 26 values was used as the pessimistic scenario, an‎d the average of the next 26 values was considered the optimistic scenario for constructing the scenario tree. The mathematical model developed in this study incorporates two objective functions: maximizing capital an‎d minimizing portfolio variance, while accounting for transaction costs. The multi-objective model was solved using the goal programming method. Applying the model to real data from ten selec‎ted stocks resulted in the optimal portfolio weight combination at each node of the scenario tree. The obtained results demonstrated the model’s capability to generate acceptable returns under various market conditions while effectively managing risk levels an‎d controlling transaction costs. Beyond introducing a multi-stage decision-making model, this research enables the eva‎luation of portfolio behavior in response to changing market conditions an‎d transaction costs. Therefore, it can serve as an effective tool for investors an‎d portfolio managers operating under market uncertainty.

مدل سازي مبتني بر گره , بهينه سازي سبدسهام چند مرحله‌اي , انتخاب پورتفوليو , درخت سناريو , عدم قطعيت , فروش استقراضي , بهينه سازي سبد سهام

Node-based modeling , multi-stage portfolio optimization , portfolio selec‎tion , scenario tree , uncertainty , short selling , portfolio optimization

Mehdi Afshari Sarkhosh

Dr. Emran Mohammadi Kelidsar