Document Type : Research Article
Authors
Department of Industrial Engineering, Payame Noor University, Tehran, Iran
Abstract
Optimizing investment portfolios by assessing efficiency in competitive environments is a vital topic in investment management. The volatility of financial markets and increasing uncertainty make it difficult to use traditional models effectively. As a result, there has been growing interest in optimizing financial models under uncertainty to better reflect real-world conditions. The present study develops a combined optimization model to evaluate risk under uncertainty in inputs and outputs. This model uses Network Data Envelopment Analysis (NDEA), robust optimization, and Lagrangian relaxation. The data for this study are the latest adjusted price data of 40 top cryptocurrencies from CoinMarketCap, used to estimate risk and create an optimal portfolio. A two-step approach is proposed to select and optimize the cryptocurrency portfolio, make the investment process more reliable, and comprehensively evaluate cryptocurrencies based on financial criteria. In the first step, the efficiency of the selected cryptocurrencies is evaluated using NDEA and robust programming. In the second step, Lagrangian relaxation is applied to handle the complicating constraints of the problem. This approach helps determine the selection of cryptocurrencies and the investment amounts, and provides a basis for allocating investment amounts. The computational results compare the direct solution of the model in GAMS with the Lagrangian relaxation algorithm on instances of increasing size.
Highlights
- Integrates NDEA, robust optimization, and Lagrangian relaxation for crypto portfolios.
- Proposes a two-stage model linking efficiency evaluation and investment allocation.
- Applies MSVG and MADG risk models under robust uncertainty conditions.
- Tests the framework on 40 top cryptocurrencies from CoinMarketCap data.
- Shows that Lagrangian relaxation outperforms CPLEX on medium- and large-scale problems.
Keywords
- Cryptocurrency
- Network data envelopment analysis
- Robust programming
- Lagrangian relaxation
- Portfolio optimization
Main Subjects
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