The digitalization of bank data and financial operations creates a large risk of loss. Losses due to the risk of errors in the bank’s digital system need to be mitigated through the readiness of reserve funds. The determination of reserve funds needs to be optimized so that there is no large excess of reserve funds. Then the rest of the reserve fund allocation can be used as an investment fund by the bank to obtain additional returns or profits. This study aims to optimize the reserve fund allocation for digital banking transactions. In this case, the decision variable is value reserved based on potential loss of each digital banking, and the objective function is defined as minimizing reserve fund allocation. Furthermore, some conditions that become limitation are rules of Basel II, Basel III, and Article 71 paragraph 1 of the Limited Liability Company Law. Since the objective function can be expressed as a linear function, in this paper, linear programming optimization approach is thus employed considering Extreme Value-at-Risk (EVaR) constraints. In the use of EVaR approach in the digital banking problem, it is found that the loss meets the criteria of extreme data based on the Generalized Pareto Distribution (GPD). The strength of reserve funds using linear programming optimization with EVaR constraints is the consideration of potential losses from digital banking risks that are minimized so that the allocation of company funds becomes optimum. While the determination of reserve funds with a standard approach only considers historical profit data, this can result in excessive reserve funds because they are not considered potential risks in the future period. For the numerical experiment, the following risk data are used in the modeling, i.e., the result of a sample simulation of digital banking losses due to the risk of system downtime, system timeout, external failure, and operational user failure. Therefore, the optimization model with EVaR constraints produces an optimal reserve fund value, so that the allocation of bank reserve funds becomes efficient. This provides a view for banking companies to avoid the worst risk, namely collapse due to unbalanced mandatory reserve funds.

Traditional mean-variance (MV) models, considered effective in stable conditions, often prove inadequate in uncertain market scenarios. Therefore, there is a need for more robust and better portfolio optimization methods to handle the fluctuations and uncertainties in asset returns and covariances. This study aims to perform a Systematic Literature Review (SLR) on robust portfolio mean-variance (RPMV) in stock investment utilizing genetic algorithms (GAs). The SLR covered studies from 1995 to 2024, allowing a thorough analysis of the evolution and effectiveness of robust portfolio optimization methods over time. The method used to conduct the SLR followed the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines. The result of the SLR presented a novel strategy to combine robust optimization methods and a GA in order to enhance RPMV. The uncertainty parameters, cardinality constraints, optimization constraints, risk-aversion parameters, robust covariance estimators, relative and absolute robustness, and parameters adopted were unable to develop portfolios capable of maintaining performance despite market uncertainties. This led to the inclusion of GAs to solve the complex optimization problems associated with RPMV efficiently, as well as fine-tuning parameters to improve solution accuracy. In three papers, the empirical validation of the results was conducted using historical data from different global capital markets such as Hang Seng (Hong Kong), Data Analysis Expressions (DAX) 100 (Germany), the Financial Times Stock Exchange (FTSE) 100 (U.K.), S&P 100 (USA), Nikkei 225 (Japan), and the Indonesia Stock Exchange (IDX), and the results showed that the RPMV model optimized with a GA was more stable and provided higher returns compared with traditional MV models. Furthermore, the proposed method effectively mitigated market uncertainties, making it a valuable tool for investors aiming to optimize portfolios under uncertain conditions. The implications of this study relate to handling uncertainty in asset returns, dynamic portfolio parameters, and the effectiveness of GAs in solving portfolio optimization problems under uncertainty, providing near-optimal solutions with relatively lower computational time.