Journal of Mathematics and Modeling in Finance

Abstract This study analyzes the trend of risk and profitability of 60 Iranian listed companies during the period of 2015 to 2022. The research data was extracted from the audited financial statements of these companies and includes key financial variables such as Debt to Equity ratio, Current Ratio, Return  on Assets (ROA), Return on Equity (ROE), Net Profit Margin, Operating Margin, and Asset Turnover. After normalizing the indicators and numerical scoring based on weighted average, the risk level of the companies was calculated. Then, using a fuzzy logic model, the impact of liquidity and asset variables on profit before tax was analyzed. The results show that most companies are at a medium to low risk level, and in some companies, an upward trend in risk has been accompanied by a decrease in profitability. The application of the fuzzy model has been able to better model the non-linear and complex relationships between financial indicators and can be useful for assessing profitability potential. In addition, to assess the stability of companies' capital structure, fluctuations in the debt-to-equity ratio were analyzed using a 3-year moving average.

Abstract The feasibility of XRP as a liquidity medium in cross-border transactions is assessed in this paper using a thorough stochastic framework. We use simulations of settlement latency, regime-switching volatility, and jump-diffusion models. The models are calibrated using historical data from public exchanges and RippleNet corridors, and they assess FX dynamics, liquidity depth, and tail risks in real-world scenarios. The behavior of XRP differs significantly from the conventional GBM assumptions, according to the results, and stochastic volatility with regime awareness provides a reliable path to corridor optimization. Our empirical validation shows that adding volatility feedback and routing adjustments significantly increases remittance success rates.

Abstract This study aims to identify the macroeconomic factors influencing the likelihood of a banking crisis in Iran, with a particular focus on macroprudential policy. We employed a discrete econometric model (Logit/Probit) using data from 2011 to 2023. The independent variables include the loan-to-deposit ratio (LTD) as a proxy for macroprudential policy, the interbank interest rate as a proxy for monetary policy, as well as the inflation rate and exchange rate volatility as indicators of macroeconomic instability. The positive and significant coefficient of LTD confirms that liquidity risk arising from excessive credit expansion is the main domestic factor increasing the probability of a crisis. The strong and positive coefficients for inflation and exchange rate volatility suggest that macroeconomic and currency shocks threaten financial stability by deteriorating asset quality and increasing loan defaults. The coefficient for the interbank rate implies the dominance of the disciplinary and supervisory effects of monetary policy over liquidity risk, meaning that a targeted increase in the policy rate by the central bank effectively reduces the probability of a crisis by imposing higher costs on riskier banks. Overall, the findings indicate that financial stability in Iran is influenced by short-term liquidity management and macroeconomic shocks, and that macroprudential policy plays an effective role in curbing risk-taking behavior.

Abstract In this paper, we study optimal control problem for stochastic systems generated by general McKean-Vlasov dynamics. The coefficients of the McKean-Vlasov dynamic depend on the state of the solution process as well as of its probability law. The information available to the controller is possibly less than the whole information. Our necessary maximum principle is established by applying Girsanov's Lemma and Lions's partial-derivatives with respect to probability law. As an application to finance, the conditional random mean-variance portfolio selection problem of McKean-Vlasov type is discussed to illustrate our theoretical results, where the optimal partially observed portfolio has been derived explicitly.

Abstract Stock price forecasting poses significant challenges due to non-stationarity, nonlinearity, and noise in financial markets, particularly for the Iraqi stock exchange. This study proposes an enhanced interval-valued forecasting model for daily prices of the Al Mansour Pharmaceutical Industries (MPI) company (2020–2025) using v-support vector regression (VSVR) with hyperparameters optimized via the waterwheel plant algorithm (WWPOA). The WWPOA approach tunes key VSVR parameters through population-based exploration and exploitation phases inspired by WWPOA, outperforming grid search (GS-VSVR) and cross-validation (CV-VSVR). Forecasting performance is evaluated using four criteria, namely mean absolute error , root mean squared error , direction accuracy and coefficient of determination . The empirical results show that the proposed model achieves lower values, compared to and indicating superior accuracy, robustness, and directional forecasting capability. On training data (637 days), WWPOA-VSVR achieves superior metrics for center and radius compared to baselines; testing results (308 days) confirm robustness. Further, Diebold-Mariano tests validate center-based WWPOA-VSVR superiority over radius-based at 95% confidence (p<0.05). On the training set, the center based WWPOA VSVR achieves MAE of about 0.18, RMSE of about 0.28, DA around 0.63, and R² close to 0.93, while the radius based model attains MAE near 0.19, RMSE around 0.29, DA about 0.61, and R² near 0.92. On the test set, center forecasts retain strong performance, with MAE around 0.20, RMSE about 0.30, DA near 0.60, and R² approximately 0.92, and radius forecasts achieve MAE close to 0.17, RMSE near 0.27, DA about 0.57, and R² around 0.88.

Abstract Value at Risk (VaR) is a key measure in financial risk management. However, traditional VaR models are often challenged by the inherent uncertainty and ambiguity in market data. This paper introduces a novel method for estimating VaR under fuzzy conditions to address this limitation. In this study, we consider a linear portfolio consisting of ten stocks whose returns are imprecise and vague. To handle this vagueness, we assume that the portfolio returns follow a normal distribution and are represented as triangular fuzzy numbers. The proposed method employs α-cut sets to compute the fuzzy VaR for the portfolio. Additionally, we use daily log returns to estimate the returns for each stock over the specified period. By applying this method, we can calculate the lower and upper bounds, as well as the core values of the α-cuts, for the fuzzy VaR metric of the portfolio. The numerical results demonstrate that fuzzy VaR yields more accurate estimates compared to traditional VaR. This study illustrates how fuzzy VaR techniques improve decision making under ambiguity by providing a more realistic representation of financial uncertainty.

Abstract In the calibration of a financial model, the process is an optimization task that can be viewed as an inverse problem. Solving this problem typically necessitates having an appropriate pricing function. With recent breakthroughs in machine learning, i.e., physics informed neural networks (PINNs), a cutting-edge approach that combines artificial neural networks with fundamental physical principles, the task can be efficiently implemented by the inverse physics-informed neural network (iPINN). This paper centers on solving an inverse problem for a financial P(I)DE model by means of iPINN. Firstly, we model the bond price dynamics of catastrophe bonds (CAT bonds) and derive a partial integro-differential equation (PIDE) through a no-arbitrage strategy within the framework of an incomplete market. Thereafter, we employ the iPINN to estimate a specific parameter of the model, namely the market price of risk. The market price of risk is treated as a global learnable parameter and is embedded directly into the PIDE operator. The proposed iPINN is evaluated through three practically meaningful criteria: repricing error, parameter stability, and PIDE residual consistency. The outcomes demonstrate that iPINNs have the capability to solve the inverse problem effectively, and this technique could be applied broadly to real-world data.

Abstract Accurate forecasting of asset returns is essential for informed investment decisions and effective portfolio management. This paper explores a hybrid model that combines the Capital Asset Pricing Model (CAPM) with Long Short-Term Memory (LSTM) networks to enhance return predictions. While CAPM traditionally estimates expected returns based on market behavior, it has limitations due to its linear assumptions and reliance on uncertain market return forecasts. In contrast, LSTM models excel at capturing complex, nonlinear relationships and temporal dependencies in financial time series data. Our study integrates LSTM forecasts of market returns into the CAPM framework, hypothesizing that this combined approach will yield superior accuracy, particularly in volatile market conditions. Through empirical analysis using five major US equities spanning 2000-2024, we demonstrate that our hybrid model outperforms traditional CAPM predictions by 23-44% in mean squared error reduction. The findings provide valuable insights for future research and practical applications in financial forecasting, highlighting the potential of deep learning techniques in asset valuation while maintaining economic interpretability.

Abstract The Pareto distribution is a cornerstone for modeling heavy-tailed phenomena in fields like economics, finance, and risk management. While maximum likelihood (ML) estimation is prevalent, its estimators lack closed-form expressions, requiring iterative numerical methods. This paper introduces closed-form estimators for the Pareto distribution using the method of logarithmic moments. The proposed estimators are computationally simple and eliminate convergence issues associated with ML. We derive their large-sample properties, establishing consistency. For comparative purposes, L-moments estimators for the Pareto distribution are also considered. A comprehensive simulation study demonstrates that the proposed logarithmic moments estimators perform competitively with ML for heavy-tailed distributions. Moreover, an empirical application to real-world fire insurance claims data confirms the practical advantages of the proposed method, where it achieves a better fit compared to ML. The combination of closed-form simplicity, competitive performance in heavy-tailed settings, and computational efficiency makes the proposed estimators a powerful and practical alternative for rapid data analysis, pedagogical purposes, and applications with limited computational resources.

Abstract This paper develops an agent-based framework for studying financial sentiment dynamics through a three-state lattice gas model in which agents hold bullish, neutral, or bearish positions. Extending classical binary models such as the Ising and voter models, the framework introduces a neutral state to capture hesitation, indecision, and temporary withdrawal from directional beliefs, especially during uncertain market conditions. Sentiment changes are driven by local interactions among neighboring agents and external information shocks, with reversible stochastic dynamics governing the updating process. Analytical results and numerical simulations show the emergence of persistent opinion clusters, entropy shifts under information stress, and gradual recovery toward balance after strong shocks. Empirical illustrations using sentiment extracted from financial social-media data suggest that the model can reproduce key patterns in market reactions. Compared with standard binary approaches, the three-state formulation better captures uncertainty, the buffering role of neutral agents, asymmetric shock responses, and recovery dynamics, making it a useful framework for linking individual sentiment updates to collective market behavior.

Abstract The aim of this work is to calculate the fair profit-sharing ratios and the expected payoffs at maturity for each partner in islamic investment contrats (or instruments), based on profit and loss-sharing (PL-sharing). These investment contracts, known as mudarabah and musharakah, can be compared to limited partnerships and joint ventures (including all types of venture, such as joint-stock companies, partnerships, etc) in conventional finance. To compute these quantities, we introduce the notion of c-fair profit-sharing ratios, where c =(c1,...,cd) ∈ (R^⋆)^d and d is the number of partners. This constitutes an equilibrium approach that accounts for the contributions of the contracting parties in terms of both capital and labour. We show that the c-fair profit-sharing ratio of each partner is the sum of their contributions to capital and labour, weighted by some economic factors that we identify as investment risk and opportunity respectively. We deduce that, in the c-fair model, the expected investment profit is distributed among the contracts partners according to the shares ϖ_ℓ = c_ℓ /(c₁ + ... + c_d), that correspond to their respective contribution weights to the venture’s overall success. We extend these results to mixed contract that combine one or both previous contracts with an agency (known as wakalah) contract.

Abstract In this paper, the credit risk of investment is managed by a new structural mean-reverting model. For this purpose, the utility maximization problem is expressed as an optimization problem with an expected logarithmic objective function and a mean-reverting constraint. The existence of a solution to the expressed problem is proved in a lemma. Moreover, one theorem for facilitating the optimal strategy design algorithm is proved. In this way, the optimal strategy is obtained for hedging the credit risk of investing in stocks of companies. Finally, the distance to default of investment is calculated by using the Black-Scholes formula for call options on wealth values obtained by optimal portfolio selection based on the proposed the optimal strategy. ‎Also, ‎the ‎stability ‎of ‎the ‎proposed ‎method ‎is ‎proved ‎in ‎the ‎second ‎theorem.‎ ‎For demonstrating the applicable results, the portfolio allocation problem is simulated by using the proposed method and compared with the non-mean-reverting equity approach. According to the simulation result, the portfolio values don’t fall and default doesn’t occur during the investment period [0, T], approximately. Also, distance to default tends to zero. ‎period [0, T], approximately. Also, distance to default tends to zero.