The purpose of this study is to propose a novel approach for measuring productivity changes in decision-making units (DMUs) over time and evaluating the performance of each DMU under uncertainty in terms of progress, regression, and stagnation. To achieve this, the Malmquist productivity index (MPI) and the data envelopment analysis (DEA) models are extended, and a new productivity index capable of handling uncertain data are introduced through a robust optimization approach. Robust optimization is recognized as one of the most applicable and effective methods in uncertain programming. The implementation and calculation of the proposed index are demonstrated using data from 15 actively traded stocks in the petroleum products industry on the Tehran stock exchange over two consecutive years. The results reveal that a significant number of stocks exhibit an unfavorable trend, marked by a decline in productivity. The findings highlight the efficacy and effectiveness of the proposed robust Malmquist productivity index (RMPI) in measuring and identifying productivity trends for each stock under data uncertainty.

In the aftermath of global financial crises and amid increasing complexity in banking operations, understanding and managing various types of risk—especially liquidity, credit, and solvency risks—has become a global concern for financial stability. This study addresses a critical gap in the literature by examining the dynamic interrelationships among these three types of risk in the context of emerging markets. Using data from 21 banks listed on the Iranian capital market from 2011 to 2023, we employ a Panel Vector Error Correction Model (VECM) alongside panel impulse response analysis to assess both short- and long-term dynamics. Our results reveal that an increase in liquidity positively impacts bank solvency, while credit risk negatively affects solvency but does not significantly influence liquidity risk. These findings contribute to the theoretical understanding of systemic risk interactions in banking and provide practical insights for policymakers and financial institutions seeking to enhance risk management strategies in volatile market environments.