This paper studies a stochastic extension of a four-dimensional nonlinear financial system describing the interaction between the interest rate, investment demand, price index, and the diffusion of financial information. Random fluctuations are introduced through multiplicative white-noise perturbations, reflecting uncertainty and external shocks inherent in real financial markets. Using tools from stochastic differential equations and Lyapunov stability theory, we establish global existence and uniqueness of positive solutions, stochastic ultimate boundedness, and sufficient conditions for global attractivity. We further derive sharp criteria for extinction and persistence in the mean of key financial variables, highlighting the stabilizing and destabilizing roles of noise intensity. The long-term dynamics are characterized by the existence of invariant probability measures and ergodicity under suitable nondegeneracy conditions. Numerical simulations based on the Euler–Maruyama scheme illustrate noise-induced transitions between chaotic persistence, stabilization, and extinction regimes, and provide quantitative support for the theoretical results. The analysis clarifies how stochastic perturbations can regulate chaotic financial dynamics and offers insight into the impact of uncertainty on macro-financial stability.
This study develops a super-efficiency fuzzy RDM-based DEA model using interval-valued Pythagorean fuzzy numbers (IVPFNs), capable of handling positive, negative, interval-valued, and fuzzy data concurrently. The framework assesses each decision-making unit (DMU) using paired optimistic and pessimistic super-efficiency models, producing an interval-valued super-efficiency score that captures both best-case and worst-case performance. Existing fuzzy DEA models are unable to simultaneously accommodate negative and IVPFN data. The novel contributions include: extending the non-radial IVPFN model to incorporate the Range Directional Measure (RDM) with negative data handling, resolving infeasibility issues through systematic slack and surplus adjustments, and pioneering the application of fuzzy DEA to air pollutant assessment with mixed data types. Empirical findings demonstrate that the proposed model produces distinct efficiency scores for most DMUs, establishing enhanced ranking capability, as substantiated by a comparative illustration showing that, in the existing IVPFN-based model, the maximum regret scores remain identical for several DMUs, resulting in reduced discriminatory power. This study presents a cross-sectional empirical analysis of 33 Indian cities for the month of May 2024, examining the principal air pollutants (PM _2.5 , PM _10 , NO _2 , and SO _2 ) in conjunction with the qualitative classification of the Air Quality Index (AQI). Computational efficiency and tractability of the proposed models are confirmed by their implementation in LINGO 20.0, which converge within 22–23 s. The proposed approach provides policymakers with robust tools for air quality performance assessment and supports evidence-based strategies for sustainable urban development and pollution mitigation.
This study presents a Bayesian optimization framework for sustainable portfolios that integrates large language model–based environmental, social, and governance (ESG) signal extraction with an extended Black–Litterman (BL) model. The framework addresses two key challenges: the inconsistency and limited coverage of traditional ESG ratings, and the static incorporation of ESG scores in portfolio models. First, ESG features are extracted from financial news via a multi-stage classification pipeline combining in-context learning with fine-tuned transformer models. Subsequently, sentiment-weighted ESG scores are benchmark-aligned with multiple rating agencies, decomposed into environmental, social, and governance dimensions, and embedded into the BL framework as structured investor views. Within the Bayesian setting, the model synthesizes market equilibrium returns with ESG-informed views to derive posterior expected returns. These posteriors drive a nonlinear Sharpe ratio maximization under realistic constraints, solved via Sequential Least Squares Programming with Ledoit–Wolf shrinkage for covariance estimation. Empirical analysis on five years of data from 64 KOSPI-listed firms demonstrates superior risk-adjusted returns, enhanced volatility control, and consistent outperformance over market benchmarks and ESG ETFs.
Cryptocurrencies are blockchain-based financial assets that exhibit high volatility due to their nonstationary and nonlinear characteristics. Accurate price forecasting of cryptocurrencies is crucial for investors and professional traders to minimize capital losses, yet it remains challenging due to their stochastic nature. Previous research suggests that integrating robust data decomposition techniques with machine learning models can enhance forecasting performance. Time series decomposition yields subseries with varying frequencies, periodicities, and noise. Existing studies employ a single forecasting model for all decomposed subseries, ignoring their heterogeneity and leading to inconsistent results in volatile markets. We propose a hybrid model for reliable and consistent Ethereum and Bitcoin price forecasting. The model utilizes Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) for data decomposition, Lempel-Ziv Complexity (LZC), and Permutation Entropy (PE) to characterize the mode complexity in the de-composed series and an Adaptive Model Selection (AMS) framework that determines the best-fitting forecasting model for each subseries from a pool of deep learning models according to the signal’s noise complexity. We use the Multi-Objective Tree Parzen estimator (MOTPE) to fine-tune the neural network hyperparameters for each subseries. We conduct extensive experiments and compare the proposed CEEMDAN-AMS model’s performance to nine benchmark models and previous studies. The proposed model outperforms its competitors and produces the most accurate and reliable short-term forecasts for Bitcoin and Ethereum. The proposed architecture can be applied to a wide range of financial and non-financial forecasting problems. While empirically validated on Bitcoin and Ethereum, the proposed architecture is designed to be applicable to various financial and non-financial forecasting problems, and its generalizability to other cryptocurrency markets warrant further empirical investigation. With contributions in entropy-based feature selection, signal-processing-based data preprocessing, and deep learning models, this work benefits researchers in econophysics, traders, and technical domains.
This paper systematically evaluates the dual effects and underlying mechanisms of China’s inaugural local government debt replacement program on mitigating local debt risks and stabilizing the real estate market. Employing an intensity Difference-in-Differences identification strategy, we integrate local governments, commercial banks, and the real estate market into a unified analytical framework. The findings reveal that: First, local government debt replacement significantly reduces the level of local government debt risk. Second, debt replacement effectively guides the stabilization of the real estate market. Mechanism analysis indicates that debt replacement acts as a stabilizer by channeling liquidity from commercial banks into the real estate sector and bolstering market confidence. However, this paper also cautions that while this strategy alleviates liquidity risks in the short term, it may potentially induce moral hazard and contribute to speculative booms in the real estate market. Consequently, this paper proposes three policy implications: dialectically evaluating the effects of replacement to prevent moral hazard; establishing precise coordination mechanisms between debt replacement and real estate regulation to curb speculation; and leveraging the window of opportunity provided by replacement to advance fiscal and tax reforms, ensuring long-term fiscal sustainability. This study enriches the literature on local debt management and offers empirical evidence and theoretical insights into the dual role of government debt instruments in mitigating local risks and stabilizing asset prices.
While accurate carbon price prediction in the EU Emissions Trading System (EU ETS) is increasingly important, existing studies often rely on static feature sets and thus overlook the time-varying effects of institutional reforms and external shocks. To address this limitation, this paper develops a forecasting approach that incorporates explainable time-varying features into the prediction process. Using daily multidimensional data spanning policy, financial, energy, and commodity variables from 2013 to 2025, a rolling explainable machine learning method is employed to trace shifts in predictor relevance over time. The evidence indicates a gradual transition from a policy-dominant to a more market-driven predictive structure across different phases of the EU ETS. To interpret these shifts more systematically, feature contributions are grouped by economic dimension, and a Systemic Fragility Index is constructed from driver concentration, realized volatility, and tail risk. Building on this evidence, the dynamically screened features are incorporated into carbon price forecasting. Compared with static alternatives, the resulting forecasts achieve higher out-of-sample accuracy and perform well against benchmark models. A supplementary trading exercise further suggests that the forecasts contain economic value under realistic trading frictions. These findings provide empirical evidence on the dynamic evolution of carbon price predictors and offer practical implications for improving carbon market forecasting and regulatory decision-making.
Using monthly panel data from January 2020 to March 2024, this study evaluates how imports of U.S. LNG changed across destination markets after the Russia–Ukraine war, from the perspective of U.S. exports. We implement a difference-in-differences design with two-way fixed effects. Within this framework, we decompose trade responses along three dimensions—value, volume, and price (PVV). We further use an event-study specification with multiple event windows and alternative control groups to assess timing patterns and robustness. Results show that, for Europe, both trade value and volume rise significantly in multiple windows. Price differentials remain persistently significant. This timing pattern suggests that Europe’s adjustment often appears first as a price premium and later as a clearer expansion in shipped volumes. In contrast, Asia does not exhibit a systematic substitution-driven expansion. Across alternative control groups, trade value and volume either decline or remain statistically insignificant, while prices stay relatively stable. The evidence is consistent with an adjustment channel that relies on existing contracts and supply diversification, with buffering achieved through changes in the composition of quantities rather than higher prices. Additional analyses indicate that the shock effects are phased and sensitive to windows choices. Europe also shows substantial within-region and cross-country heterogeneity in the “volume–price mix,” implying that transmission routes are constrained by structural conditions in each market. This study contributes by decomposing overall trade changes into quantity and price components within a unified identification strategy, and by using dynamic evidence to characterize adjustment speed and regional heterogeneity.
Machine learning methods outperform traditional theoretical models in predictive performance but often face challenges with explainability and transparency. To address these challenges, this study proposes an interpretable machine learning framework for predicting auto insurance renewals and understanding the behavioral and economic factors that drive customer decisions. Using a dataset of 65,535 auto insurance records from 2016 to 2019, a Random Forest (RF)–based binary classification model is developed and demonstrated the highest predictive performance compared with the Naïve Bayes (NB) and K-Nearest Neighbors (KNN) algorithms, achieving the top scores across five key metrics: True Negative Rate (TNR), Positive Predictive Value (PPV), False Positive Rate (FPR), Matthews Correlation Coefficient (MCC), and Kappa coefficient. By integrating feature importance analysis, Partial Dependence Plot (PDP), and Local Interpretable Model-Agnostic Explanations (LIME), the study reveals that new car purchase price, signed premium, insured person’s age, and car age are the dominant factors influencing renewal decisions. Specifically, customers with 1–2-year-old vehicles, signed premiums in either low or high price segments, and new car purchase prices above 200,000 yuan are more likely to renew their insurance policies. Overall, this study bridges predictive accuracy with interpretability to generate actionable insights for customer retention, offering data-driven guidance for dynamic policy pricing, flexible resource allocation, and targeted market strategies. The random forest algorithm outperforms other models in predicting car insurance renewal. New car price, signed premium, insured age, and car age significantly impact prediction outcomes. Insurance renewal rates are directly linked to customer needs. A higher car purchase price is correlated with an increased probability of customer renewal. New car customers with vehicles aged 1-2 years are more likely to renew their insurance policies.
Accurate forecasting of stock index trends remains challenging because financial time series are noisy, volatile, and non-linear. This study proposes a denoising–prediction–explanation pipeline for next-day trend prediction of the Nifty 50 index. First, an adaptive Kalman filter (AKF) reduces measurement noise in the closing-price series while preserving turning points. Second, we train a deep clockwork recurrent neural network (DCWRNN) that updates hidden modules at multiple temporal resolutions and uses lagged technical indicators as predictors. Third, we apply SHapley Additive exPlanations (SHAP) to quantify how each lagged indicator and price lag contributes to forecasts and to link these drivers to forecast error and trading performance. On the normalized close-price target, the long short-term memory model with AKF preprocessing achieves the lowest point-forecast errors (mean absolute error MAE = 0.000462; root mean squared error RMSE = 0.000589), while DCWRNN with AKF delivers the strongest trading performance. In backtesting, the DCWRNN(AKF) strategy attains 49.46
The interconnected structure of energy markets plays a pivotal role in shaping the transmission and spillover of risk across markets. This research contributes to the existing literature by investigating the dynamic connectedness among energy markets using various financial energy-related indices: renewable (solar, wind, biofuels, geothermal), fossil (oil, gas, coal), and nuclear. The empirical analysis employs a time-varying quantile connectedness framework to identify tail dependence and risk spillover dynamics among the aforementioned energy markets. The findings suggest that connectedness increases during extreme downside (Q = 0.05) and upside (Q = 0.95) conditions. Renewable energy, particularly solar and biofuels, and nuclear markets act as primary shock transmitters during periods of high stress. In contrast, coal and gas markets tend to receive shocks, while the oil market remains neutral. Under normal conditions (Q = 0.50), total connectedness decreases to 28.40
This paper proposes a model-free delta hedging framework for multi-period option hedging, addressing the optimization dilemma between hedging accuracy and transaction costs by integrating deep reinforcement learning (DRL) with a terminal profit-and-loss (P L) objective function. To enhance the stability and interpretability of DRL-based hedging, we introduce a novel strategy (DQN-BS) that leverages neural networks to fit the residual between the market-implied actual delta and the Black-Scholes (BS) delta, thereby combining the theoretical foundation of BS pricing with the adaptive learning capability of DRL. Using daily data of SSE 50ETF options (2019–2025) and S P 500 ETF options (2021–2025), we conduct empirical tests across zero, low, and high transaction cost scenarios, covering both call and put options under normal and high-volatility market regimes (e.g., the COVID-19 pandemic period). The results demonstrate that DQN-BS outperforms traditional BS Delta hedging and standard DQN strategies in three key dimensions: (1) higher average P L and win rate (up to 72.81
Bitcoin and other cryptocurrency markets are volatile by nature, which provides an opportunity as well as a threat to an investor and researcher. The correct forecasting of prices is an important factor in making informed decisions when in such dynamic conditions. The paper presents a explainable LIM-GRLST framework of Bitcoin price forecasting on a one-step-ahead basis with deep learning. The baseline LSTM and GRU models were trained initially and then hybrid models that combine the complementary advantages of the two models were trained. A weighted hybrid also exhibited relatively small improvements, whereas the neural hybrid produced the highest results (MAE = 0.0209, MSE = 0.0008, RMSE = 0.0279, R 2 = 0.9897), which were tested on an unknown test set. Standard post-hoc methods, permutation importance and LIME, were used to provide the feature-level explainability, indicating closing, high, and low prices as the most important predictors. The article focuses on enhancing engineering within frameworks of hybrid and hyperparameter optimization over a novel methodology, and is shown to be applicable in practice to cryptocurrency forecasting.
The paper proposes the use of the Laplace approximation in Bayesian estimation of complex univariate symmetric and asymmetric stochastic volatility models with flexible distributions for standardised returns. We show how easily the Laplace approximation can be used to estimate complex stochastic volatility models, requiring only minor adjustments to the code when changing model specifications, priors, or sampling error distributions. Using a simulation study, we show that the Laplace approximation provides parameter estimates that are close to the true values in finite samples while remaining computationally competitive with traditional Bayesian and data cloning estimators, being the fastest of the three for small samples and trading some speed for robustness and ease of implementation as the sample size grows. This approach provides an effective alternative to existing methods for estimating stochastic volatility models. Furthermore, we evaluate the performance of the models in-sample and out-of-sample by forecasting volatility one-day-ahead. For this purpose, we use four well-known series of energy indices, two for clean energy and two for conventional (brown) energy. In the out-of-sample analysis, we investigate how the model’s performance in predicting volatility is affected by climate policy uncertainty and energy prices. Our results show the advantage of using asymmetric stochastic volatility models for clean energy indices, while symmetric stochastic volatility models provide competitive performance for brown energy indices.
In the era of data-driven decision-making, stochastic frontier models (SFMs) have become a powerful tool for analyzing production efficiency across various domains. While model averaging is an effective strategy to mitigate model misspecification and enhance prediction accuracy, existing approaches often overlook the risks of individual privacy leakage during the model weighting process. To address this challenge, we propose a novel differentially private model averaging framework for stochastic frontier models. We develop two variants of differentially private Frank-Wolfe algorithms tailored to low-to-moderate and high-dimensional candidate model spaces, respectively, achieving a favorable trade-off between privacy protection and estimation accuracy. Our method integrates differential privacy guarantees into the weight optimization procedure via perturbation mechanisms and privacy-aware algorithms,such as a private variant of the Frank-Wolfe algorithm. We further analyze both theoretical utility bounds and empirical performance under various privacy budgets. Simulation studies demonstrate that our approach achieves a favorable balance between prediction accuracy and privacy protection, outperforming baseline regularization methods in scenarios with high model uncertainty.
Systemic risk monitoring and early warning systems for commercial banks are essential for maintaining financial stability and enhancing regulatory effectiveness. This study presents an innovative framework that integrates sentiment analysis with deep learning architectures to significantly improve risk prediction accuracy. We develop a novel sentiment index using text mining techniques applied to online public opinion data, combined with Time-Varying Parameter Vector Autoregression (TVP-VAR) modeling to capture dynamic inter-bank sentiment spillovers. This sentiment index is subsequently incorporated into a comprehensive risk early warning system powered by a Bidirectional Long Short-Term Memory network with Attention Mechanism (BiLSTM-AM). Our empirical analysis, based on data from 24 Chinese commercial banks (2017–2023), demonstrates substantial improvements: the BiLSTM-AM model reduces Mean Squared Error (MSE) by 25.2
Financial markets are becoming more interconnected, leading to a better understanding of how shocks can spread across different markets. Investor sentiment is crucial in market dynamics, especially during high volatility. However, traditional mean-based connectedness measures fail to capture asymmetric dependence and tail-risk dynamics and are therefore less suitable under extreme market conditions, such as crises or periods of heightened uncertainty. Against this backdrop, this study employs a quantile connectedness approach to analyze the transmission of shocks among ten financial indices, including a crypto assets-related index and an economic-news-related sentiment index. The results show significant changes in shock transmission patterns, with the Daily News Sentiment Index (DNSI) being the primary transmitter during bull markets, reinforcing the influence of news sentiment on investor behavior. Traditional indices like MSCI USA (MSCI_USA) and MSCI Europe (MSCI_EUR) are key transmitters in bear and normal market conditions, while MSCI China (MSCI_CN) and the Dow Jones Commodity Index (DJCI) are more sensitive to external shocks and act as net receivers. Furthermore, the dynamic analysis highlights the evolving role of sentiment-based indicators, particularly in extreme market regimes, supporting the role of sentiment-driven contagion effects and emphasizing their relevance for risk management. These findings highlight the importance of sentiment and traditional and emerging markets in risk management and portfolio diversification for investors and policymakers.
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.
For regulators, investors, and risk managers, the prediction of sector returns in financial markets remains a complex task. The main challenge lies in the accurate representation of the tricky interdependencies within sectors and the nonlinear dynamics that are manipulated by economic disruptions, market attitude, and structural transformations. This study conducts a comparative analysis of two major modeling paradigms for predicting sector-level returns in the context of an emerging market. The results reveal that LSTM models demonstrate superior accuracy in capturing non-linear short-term fluctuations, particularly during periods of market stress. In addition to offering insights into the sectoral behavior of an emerging economy during crisis and recovery phases, the research outlines several methodological and practical implications for portfolio management, stress-testing, and real-time economic monitoring. Future extensions include validation on other markets, integration of exogenous macroeconomic variables, and deployment of real-time adaptive forecasting systems.
According to Mandelbrot, financial assets are characterized by two characteristic traits—discontinuity and price persistence. This paper uses simulations to obtain predictions for these two key features derived from a multifractal model of asset returns (MMAR). Following Mandelbrot, this paper uses the exponents of power laws to study asset return discontinuity, whereas the level of price persistence is measured via Hurst exponents. Using the distributions of these exponents derived from MMAR simulations, this study proposes a novel joint test designed to examine whether the MMAR is capable of describing the return data on financial assets with respect to these two key traits. Intriguingly, empirical tests suggest that the benchmark MMAR specification employed here is capable of describing discontinuity and persistence observed for the returns on five key financial asset markets—U.S. equities, USD/GBP exchange rates, gold futures, crude oil futures and Bitcoin. From a theoretical perspective, the findings are consistent with the possibility that common latent mechanisms, including herding behavior, may contribute to return dynamics across otherwise unrelated asset markets.
