Deterministic and Stochastic Modeling of Deposit–Loan Dynamics with Optimal Regulatory Control

Optimal Funds in Commercial Banks Using Linear Programming

Determining Insolvency Regions in Banks: A Stochastic Dynamic Approach Integrating Liquidity and Credit Risk

We develop a continuous-time structural dynamic model to determine the exact insolvency regions of banks arising from the non-linear interaction between liquidity and credit risk. While existing literature predominantly treats these risks in isolation or via reduced-form specifications, we explicitly model the feedback loop where funding shocks and regulatory constraints force balance-sheet adjustments that can lead to endogenous insolvency. By incorporating Basel III regulatory requirements (LCR and NSFR) into a stochastic optimal control framework, we solve for the exact insolvency boundary using the Hamilton-Jacobi-Bellman (HJB) equation. To bridge the gap between theoretical complexity and supervisory practice, we derive and validate a surrogate analytical approximation function that allows for real-time monitoring. Calibrated using granular balance-sheet data from the Iranian banking sector, our model reveals significant non-linear threshold effects: the joint occurrence of liquidity stress and credit portfolio defaults disproportionately accelerates the transition toward insolvency compared to their individual effects. The proposed surrogate function offers supervisors a computationally efficient tool for stress testing and early warning systems. Our findings provide novel insights into financial frictions in emerging markets and offer a rigorous framework for integrated risk management.

A Linear Ordinary Differential Equation Model of Assets and Loan Liquidity Management of Credit Unions: A Two-state Dynamic Model

This study proposes a closed-system linear ordinary differential equation (ODE) model to analyse and predict the dynamics of liquid assets and outstanding loans in credit union liquidity risk management. Using 40 quarterly observations (2015–2024) obtained from the Central Finance Facility (CFF) of the Ghana Co-operative Credit Unions Association (CUA), the study formulates a two-state deterministic model governed by the asset-to-loan transition rate α, the loan-to-asset recovery rate β, and the loan default rate δ. Closed-form solutions are derived using the Laplace transform technique, and discrete quarterly prediction equations are obtained using a first-order Taylor expansion. Stability analysis confirms that the system is asymptotically stable when α, β, and δ are positive. Model performance is evaluated using root mean square error (RMSE), mean absolute percentage error (MAPE), and the Scatter Index (SI). The optimal asset prediction model corresponds to α = 0.0869 (MAPE = 14.27%), and the optimal loan model to ω = 0.91 (RMSE = 225,548.63). Additionally, three machine-learning models—Support Vector Regression (SVR), XGBoost, and Random Forest—are employed to generate eight-quarter-ahead forecasts (2025–2026). SVR achieves the best out-of-sample performance for forecasting both assets (MAPE = 2.92%) and loans (MAPE = 3.70%). The study concludes that the ODE-based closed liquidity model provides an analytically rigorous and practically interpretable framework for credit union liquidity planning, and that SVR-based forecasting offers a useful complement for short-term projections.

Excess Liquidity, Moral Hazard, and Credit Risk in Indonesian Commercial Banks

This research investigates how liquidity creation induces moral hazard behavior and affects credit quality in Indonesian commercial banks. This study examines the effect of liquidity creation, liquidity risk, and central bank policies on credit risk in Indonesian commercial banks, proxied by the non-performing loan (NPL) ratio. Using panel data from 46 banks listed on the Indonesia Stock Exchange over 2015–2024, we apply the Two-Step System Generalized Method of Moments (SYS-GMM) to address endogeneity inherent in dynamic panel models. Results indicate that liquidity creation has a significant positive effect on NPL, consistent with the moral hazard hypothesis. Liquidity risk (LDR) also significantly and positively affects NPL. Reserve requirements (GWM) and BI-Rate do not produce a direct and significant effect on NPL. Return on assets (ROA) significantly and negatively affects NPL. These results suggest that credit risk in Indonesian commercial banking is predominantly influenced by bank-level intermediation behavior rather than by macroeconomic or policy variables. The research concludes that excess liquidity conditions incentivize aggressive credit expansion without proportionate attention to borrower quality, particularly in an oligopolistic market structure with implicit state guarantees.

Heuristic Stochastic Controller for Stabilizing Exchange Rate Dynamics Under Uncertainty

In this paper, we develop the Stochastic Central Bank Exchange Rate Intervention (SCERI) model, based on two stochastic differential equations represented by two different Arithmetic Brownian Motions. The aim is to mathematically denote the noise from noise traders and the central bank interventios, which is a stochastic controller to assist effective policy decisions. To address SCERI’s challenges, we propose time varying target zones and values in order to support central banks to limit uncertainty. While these interventions can increase stability in the process, they require calibration of the various bounds or they may create instability. Even though there are concerns about intervention risks, our model is certainly feasible to alleviate the complications of stabilizing the currency. The proposed heuristic stochastic controller operates under the influence of noise traders, market participants whose actions cause the random fluctuations. With the use of this model and algorithm, central banks have essential tools to stabilize exchange rate dynamics as the model allows the adjustment of intervention strategies to counteract market uncertainty.

Macro-financial changes in the Russian economy

Subject. The relationship between the dynamics of the money supply, the government debt market, the structure of banking assets and monetary policy cycles. Objectives. Identify structural shifts in the financial system, assess their impact on the formation of macrofinancial risks and opportunities, and provide scientifically sound forecasts and recommendations for regulators. Methods. The study is based on econometric modeling, comparative analysis of structural components, and a method of extrapolating identified trends to build scenario forecasts. Results. A parallel exponential growth of the monetary base and the volume of the federal loan bond market has been revealed, accompanied by a sharp reduction in the participation of non-residents, which signals the formation of a sovereign financing model. Multidirectional trends in the structure of banking assets have been identified: steady growth in lending to the corporate and retail sectors, explosive growth in interbank transactions and high cyclical volatility of other items. The cyclical nature of monetary policy is determined, with phases of sharp tightening and prolonged periods of negative and high positive real interest rates. A new configuration has been established in the financial system, characterized by an increased role of internal sources of financing and credit expansion, while generating fundamental risks: inflationary pressure from an increase in the money supply, an increasing debt burden on the budget and the private sector, and a decrease in investor diversification. Conclusions. The novelty of the study lies in substantiating the need for regulators to implement a comprehensive policy balancing between liquidity sterilization, macroprudential control over credit risks, the development of the domestic capital market and cyclical monetary policy easing.