Reserve Fund Optimization Model for Digital Banking Transaction Risk with Extreme Value-at-Risk Constraints
Abstract
:1. Introduction
2. Literature Overview
2.1. Digital Banking Transaction Risk
2.2. Digital Banking Reserve Fund
3. Materials and Methods
3.1. Materials
3.2. Methods
3.2.1. Threshold Selection
3.2.2. Generalized Pareto Distribution (GPD)
3.2.3. Extreme Value-at-Risk (EVaR)
3.2.4. Linear Programming Optimization Modeling
- (a).
- Determination of Decision VariablesIn an optimization problem, it must first be stated what variables are to be determined as the result of optimization. For example, if there is a decision of n measurable variables, then can be formed as a decision variables. The value of the decision variable will be determined based on the optimization result.
- (b).
- Determination of Objective FunctionOptimization problems require an objective function as the optimum result in the form of maximization or minimization. The formulation of the objective function is based on the size of the cost coefficient of the decision variable corresponding to the problem to be solved (for example, as ). The objective function in linear programming can be written in standard form as follows:
- (c).
- Determination of Constraint FunctionOptimization problems must have limitations that affect the decision variables. The limitations of the decision variables need to be formed in a constraint function. The formulation of the constraint function is based on the technology coefficient (for example, as for and ) and right-hand-side constraints (for example as for ). In addition, in optimization problems, there are non-negativity constraints which indicate that all decision variables must have values equal to or greater than zero. Therefore, the constraint function in linear programming can be written in standard form in Equations (5) and (6).
4. Results
4.1. Reserve Fund Using EVaR
- (a).
- Ensuring that the value reserved based on potential digital banking system risk losses should not be less than the estimated digital banking losses ();
- (b).
- Ensuring that the value reserved based on potential digital banking operational risk losses should not be less than the estimated digital banking losses ();
- (c).
- Guaranteeing that the total value reserved based on potential digital banking loss must not exceed the average profit value of the digital banking itself;
- (d).
- Ensuring that the reserve based on the estimated loss of digital banking risk must not be less than the 20% () weight of the capital () for the implementation of digital banking. The weight coefficient has been set at 20% based on Article 71 paragraph 1 of the Company Law.
4.2. Reserve Fund Optimization Model Using Constraint of EvaR
4.3. Computational Solution of Reserve Fund Optimization Model
4.3.1. Profit and Capital Data on the Implementation of E-Banking Services
4.3.2. Data Simulation for Digital Banking Risk
4.3.3. Solution of Reserve Fund Optimization
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Authors | Variables | Method | Use of Value-at-Risk | Use of EVT Approach | Determination of Optimum Reserve Fund |
---|---|---|---|---|---|
Gilli and Kellezi, 2006 [18] | Market risk, and daily returns of some portfolios. | VaR, EVT, and expected shortfall. | - | Yes | - |
Esterhuysen et al., 2008 [12] | Operational losses, net interest income, and gross income. | OpVaR, SA, and AMA. | Yes | - | - |
Yao et al., 2013 [14] | Operational risks of commercial bank. | CVaR, EVT, and peak value method. | Yes | Yes | - |
Schalkwyk and Witbooi, 2017 [11] | Cumulative cost, net cash flows, and deposit risk. | Portfolio, stochastic optimal control | Yes | - | - |
Saputra et al., 2022 [10] | Digital Banking Transaction Operational Risk | Extreme Value-at-Risk | Yes | Yes | - |
Tran and Tran, 2023 [15] | Risks of global financial crisis | Value-at-Risks, GARCH | Yes | - | - |
Kyoud et al., 2023 [16] | Systemic risks of banking company | CVaR, Extreme approach | Yes | Yes | - |
Chikobvu and Ndlovu, 2023 [17] | Exchange rates risks (ZAR/USD and BTC/USD) | VaR, GEVD | Yes | Yes | - |
This Research | Digital Banking Transaction Risk | Extreme Value-at-Risk, Linear Programming Optimization | Yes | Yes | Yes |
Digital Banking Services | Profit of 2020 | Profit of 2021 | Profit of 2022 |
---|---|---|---|
Internet Banking | 2,467,284 | 4,360,382 | 5,059,046 |
Mobile Banking | 2,800,607 | 2,552,457 | 2,616,315 |
Total of Profit per Year | 5,267,891 | 6,912,839 | 7,711,361 |
Digital Banking Services | Average Profit |
---|---|
Internet Banking | 3,962,237.33 |
Mobile Banking | 2,656,459.67 |
Total of Average Profit | 5,618,697 |
Digital Banking Services | Capital |
---|---|
Internet Banking | 4,437,864.10 |
Mobile Banking | 3,569,658.65 |
Total of Capital | 8,007,522.75 |
Digital Banking Risk | Risk Type | Lots of Data after Simulation | Lots of Data above Threshold (Extreme Data) | Threshold | Parameter Estimated Value | |
---|---|---|---|---|---|---|
System Risks | Timeout System | 2000 | 300 | 56,769,000,000 | 0.05963 | |
Downtime System | 2000 | 300 | 146,258,625,357 | 73,777,000,000 | 0.09501 | |
Operational Risks | External Failure | 2000 | 300 | 35,954,062,029 | 18,913,000,000 | −0.09309 |
User Failure | 2000 | 300 | 20,768,602,154 | 7,546,800,000 | −0.14352 |
Digital Banking Risk | Risk Type | EVaR |
---|---|---|
System Risks | Timeout System | IDR 269,082,483,221.22 |
Downtime System | IDR 374,106,598,772.46 | |
Operational Risks | External Failure | IDR 81,225,609,878 |
User Failure | IDR 37,702,356,747 |
Digital Banking Risk | Risk Type | Potential Loss | Reserves |
---|---|---|---|
System Risks | Timeout System | IDR | IDR |
Downtime System | IDR | ||
Operational Risks | External Failure | IDR | IDR |
User Failure | IDR | ||
Average Proportion of Profit Reserved | IDR | ||
Total of Optimum Reserve Fund for E-Banking Risk | IDR |
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Saputra, M.P.A.; Chaerani, D.; Sukono; Md. Yusuf, M. Reserve Fund Optimization Model for Digital Banking Transaction Risk with Extreme Value-at-Risk Constraints. Mathematics 2023, 11, 3507. https://doi.org/10.3390/math11163507
Saputra MPA, Chaerani D, Sukono, Md. Yusuf M. Reserve Fund Optimization Model for Digital Banking Transaction Risk with Extreme Value-at-Risk Constraints. Mathematics. 2023; 11(16):3507. https://doi.org/10.3390/math11163507
Chicago/Turabian StyleSaputra, Moch Panji Agung, Diah Chaerani, Sukono, and Mazlynda Md. Yusuf. 2023. "Reserve Fund Optimization Model for Digital Banking Transaction Risk with Extreme Value-at-Risk Constraints" Mathematics 11, no. 16: 3507. https://doi.org/10.3390/math11163507
APA StyleSaputra, M. P. A., Chaerani, D., Sukono, & Md. Yusuf, M. (2023). Reserve Fund Optimization Model for Digital Banking Transaction Risk with Extreme Value-at-Risk Constraints. Mathematics, 11(16), 3507. https://doi.org/10.3390/math11163507