Negative data

The purpose of this study is to develop portfolio optimization and assets allocation using our proposed models. The study is based on a non-parametric efficiency analysis tool, namely Data Envelopment Analysis (DEA). Conventional DEA models assume non-negative data for inputs and outputs. However, many of these data take the negative value, therefore we propose the MeanSharp-βRisk (MShβR) model and the Multi-Objective MeanSharp-βRisk (MOMShβR) model base on Range Directional Measure (RDM) that can take positive and negative values. We utilize different risk measures in these models consist of variance, semivariance, Value at Risk (VaR) and Conditional Value at Risk (CVaR) to find the best one as input. After using our proposed models, the efficient stock companies will be selected for making the portfolio. Then, by using Multi-Objective Decision Making (MODM) model we specified the capital allocation to the stock companies that selected for the portfolio. Finally, a numerical example of the Iranian stock companies is presented to demonstrate the usefulness and effectiveness of our models, and compare different risk measures together in our models and allocate assets.

In this paper, we present a comprehensive approach for evaluating efficiency in complex networks by integrating network data envelopment analysis (NDEA) with the Malmquist productivity index. The proposed method addresses the inherent challenge of accommodating negative data within the network efficiency evaluation framework, which is a common occurrence in real-world network operations. Through the introduction of a two-stage structure, the model not only effectively manages the presence of negative values, but also provides a robust and insightful assessment of network efficiency. A case study from banking sector is employed to demonstrate the efficacy of the proposed approach, showcasing its capacity to offer valuable and actionable insights for decision-making in complex network environments. The results highlight the practical applicability and importance of the extended approach in addressing the complexities associated with evaluating efficiency in diverse network settings.