This study contributes to develop a framework to measure the financial performance of banks in a stochastic setting. The framework comprises several steps, the first of which is the development of a financial performance measurement model to evaluate a bank's financial performance using a set of factors from the CAMEL (Capital adequacy, Assets, Management Capability, Earning and Liquidity) system. Second, the stochastic setting of the efficiency measurement is handled using the data collection budget allocation approach, whereby Monte Carlo simulations are used to analyse additional generated data and a genetic algorithm is used to refine the accuracy of the efficiency estimates. The results show that the accuracy of the model is greatly improved using the proposed approach. In contrast to the conventional deterministic model, the proposed framework is more useful to managers in determining the bank's future financial operations to improve the overall financial soundness of the bank. ) should not be used; instead, they have shown that BCC formulation of Banker, Charnes, and Cooper (1984) must be applied when input and/or output include a ratio variable. Emrouznejad and Amin (2009) highlighted the convexity problem in the standard production possibility set (PPS) and suggested alternative DEA models in the presences of output ratios and/or input ratios. DEA was used by Halkos and Salamouris (2004) to derive a composite index based on the standard ratio measures of bank financial performance. Relying on this index, they evaluated the performance of Greek banks over the period 1997-1999. With regard to zero values and negative values in the DEA model, the main assumption in all DEA models was that, theoretically, all input and output values are positive, but in practice we encounter many cases that violate this term, and we ultimately have negative inputs and outputs. Among the proposed methods of dealing with negative data, the following models have been provided. Seiford and Zhu (2002) considered a positive and very small value of negative output. Another method, proposed by Halme, Pro, and Koivu (2002), offered the measurement theory and deference of scale variables and the fraction to explain the reason for negative observations and also represented a reliable method for assessing interval scale units. The modified slack-based measure model, called MSBM, was presented by Sharp, Lio, and Meng (2006). However, the latest method of behaviour with negative data was provided by Emrouznejad, Anouze, and Thanassoulis (2010); this is based on the semi-oriented radial measure model and considered some variables that are both negative and positive for DMUs.
STOCHASTIC EFFICIENCY