Search Results (11)

Transparent reasoning and interpretability are essential for AI-supported risk assessment, yet it remains unclear whether large language models (LLMs) can provide reliable, deterministic support for safety-critical tasks or merely simulate reasoning through plausible outputs. This study presents a systematic, multi-model empirical evaluation of reasoning-capable LLMs applied to machinery functional safety, focusing on Required Performance Level (PL_r) estimation as defined by ISO 13849-1 and ISO 12100. Six state-of-the-art models (Claude-opus, o3-mini, o4-mini, GPT-5-mini, Gemini-2.5-flash, DeepSeek-Reasoner) were evaluated across six prompting strategies and two dataset variants: canonical ISO-style hazards (Variant 1) and engineer-authored free-text scenarios (Variant 2). Results show that rule-grounded prompting consistently stabilizes performance, achieving ceiling-level accuracy in Variant 1 and restoring reliability under lexical variability in Variant 2. In contrast, unconstrained chain-of-thought reasoning (CoT) and CoT together with Retrieval-Augmented Generation (RAG) introduce volatility, overprediction biases, and model-dependent degradations. Safety-critical coverage was quantified through per-class F1 and recall of PL_r class e, confirming that only rule-grounded prompts reliably captured rare but high-risk hazards. Latency analysis demonstrated that rule-only prompts were both the most accurate and the most efficient, while CoT strategies incurred 2–10× overhead. A confusion/rescue analysis of retrieval interactions further revealed systematic noise mechanisms such as P-inflation and F-drift, showing that retrieval can either destabilize or rescue cases depending on model family. Intermediate severity/frequency/possibility (S/F/P) reasoning steps were found to diverge from ISO-consistent logic, reinforcing critiques that LLM “reasoning” reflects surface-level continuation rather than genuine inference. All reported figures include 95% confidence intervals, t-intervals across runs ($r=5$) for accuracy and timing, and class-stratified bootstrap CIs for Micro/Macro/Weighted-F₁ and per-class metrics. Overall, this study establishes a rigorous benchmark for evaluating LLMs in functional safety workflows such as PL_r determination. It shows that deterministic, safety-critical classification requires strict rule-constrained prompting and careful retrieval governance, rather than reliance on assumed model reasoning abilities. Full article

Navigating the complexity of petroleum futures markets—marked by extreme volatility, geopolitical uncertainty, and macroeconomic shocks—demands adaptive and risk-sensitive strategies. This paper explores an Adaptive Risk-sensitive Transformer-based Deep Reinforcement Learning (ART-DRL) framework to improve portfolio optimization in commodity futures trading. While deep reinforcement learning (DRL) has been applied in equities and forex, its use in commodities remains underexplored. We evaluate DRL models, including Deep Q-Networks (DQN), Proximal Policy Optimization (PPO), Advantage Actor-Critic (A2C), and Deep Deterministic Policy Gradient (DDPG), integrating dynamic reward functions and asset-specific optimization. Empirical results show improvements in risk-adjusted performance, with an annualized return of 1.353, a Sharpe Ratio of 4.340, and a Sortino Ratio of 57.766. Although the return is below DQN (1.476), the proposed model achieves better stability and risk control. Notably, the models demonstrate resilience by learning from historical periods of extreme volatility, including the COVID-19 pandemic (2020–2021) and geopolitical shocks such as the Russia–Ukraine conflict (2022), despite testing commencing in January 2023. This research offers a practical, data-driven framework for risk-sensitive decision-making in commodities, showing how machine learning can support portfolio management under volatile market conditions. Full article

In this paper, we consider the time-fractional Black–Scholes model with deterministic, time-varying coefficients. These time parametric constituents produce a model with greater flexibility that may capture empirical results from financial markets and their time-series datasets. We make use of transformations to reduce the underlying model to the classical heat transfer equation. We show that this transformation procedure is possible for a specific risk-free interest rate and volatility of stock function. Furthermore, we reverse these transformations and apply one-dimensional optimal subalgebras of the infinitesimal symmetry generators to establish invariant solutions. Full article

The accurate forecasting of metal prices is of great importance to industrial producers as the supply of metal raw materials is a very important part of industrial production. The futures market is subject to many factors, and metal prices are highly volatile. In the past, most of the relevant research has focused only on deterministic point forecasting, with less research performed on interval uncertainty forecasting. Therefore, this paper proposes a novel forecasting model that combines point forecasting and interval forecasting. First, a novel hybrid price point forecasting model was established using Variational Modal Decomposition (VMD) and a Long Short-Term Memory Neural Network (LSTM) based on Sparrow Search Algorithm (SSA) optimization. Then, five distribution functions based on the optimization algorithm were used to fit the time series data patterns and analyze the metal price characteristics, Finally, based on the optimal distribution function and point forecasting results, the forecasting range and confidence level were set to determine the interval forecasting model. The interval forecasting model was validated by inputting the price data of copper and aluminum into the model and obtaining the interval forecasting results. The validation results show that the proposed hybrid forecasting model not only outperforms other comparative models in terms of forecasting accuracy, but also has a better performance in forecasting sharp fluctuations and data peaks, which can provide a more valuable reference for producers and investors. Full article

This paper discusses the generalized Black-Scholes-Merton model, where the volatility coefficient, the drift coefficient of stocks, and the interest rate are time-dependent deterministic functions. Together with it, we make the assumption that the volatility, the drift, and the interest rate depend on a gamma or inverse-gamma random variable. This model includes the models of skew Student’s t- and variance-gamma-distributed stock log-returns. The price of the European forward-start call option is derived from the considered models in closed form. The obtained formulas are compared with the Black-Scholes formula through examples. Full article

This paper used different risk management indicators applied to the investment optimization performed by consumers in Distributed Generation (DG). The objective function is the total cost incurred by the consumer including the energy and capacity payments, the savings, and the revenues from the installation of DG, alongside the operation and maintenance (O&M) and investment costs. Probability density function (PDF) was used to model the price volatility in the long-term. The mathematical model uses a two-stage stochastic approach: investment and operational stages. The investment decisions are included in the first stage and which do not change with the scenarios of the uncertainty. The operation variables are in the second stage and, therefore, take different values with every realization. Three risk indicators were used to assess the uncertainty risk: Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR), and Expected Value (EV). The results showed the importance of migration from deterministic models to stochastic ones and, most importantly, the understanding of the ramifications of every risk indicator. Full article

In order to improve the prediction accuracy of wind speed, this paper proposes a hybrid wind speed prediction (WSP) method considering the fluctuation, randomness and nonlinear of wind, which can be applied to short-term deterministic and interval prediction. Variational mode decomposition (VMD) decomposes wind speed time series into nonlinear series Intrinsic mode function 1 (IMF1), stationary time series IMF2 and error sreies (ER). Principal component analysis-Radial basis function (PCA-RBF) model is used to model the nonlinear series IMF1, where PCA is applied to reduce the redundant information. Long short-term memory (LSTM) is used to establish a stationary time series model for IMF2, which can better describe the fluctuation trend of wind speed; mixture Gaussian process regression (MGPR) is used to predict ER to obtain deterministic and interval prediction results simultaneously. Finally, above methods are reconstructed to form VMD-PRBF-LSTM-MGPR which is the abbreviation of hybrid model to obtain the final results of WSP, which can better reflect the volatility of wind speed. Nine comparison models are built to verify the availability of the hybrid model. The mean absolute percentage error (MAE) and mean square error (MSE) of deterministic WSP of the proposed model are only 0.0713 and 0.3158 respectively, which are significantly smaller than the prediction results of comparison models. In addition, confidence intervals (CIs) and prediction interval (PIs) are compared in this paper. The experimental results show that both of them can quantify and represent forecast uncertainty and the PIs is wider than the corresponding CIs. Full article

The main characteristics of the photovoltaic (PV) output power are the randomness and uncertainty, such features make it not easy to establish an accurate forecasting method. The accurate short-term forecasting of PV output power has great significance for the stability, safe operation and economic dispatch of the power grid. The deterministic point forecast method ignores the randomness and volatility of PV output power. Aiming at overcoming those defects, this paper proposes a novel hybrid model for short-term PV output power interval forecasting based on ensemble empirical mode decomposition (EEMD) as well as relevance vector machine (RVM). Firstly, the EEMD is used to decompose the PV output power sequences into several intrinsic mode functions (IMFs) and residual (RES) components. After that, based on the decomposed components, the sample entropy (SE) algorithm is utilized to reconstruct those components where three new components with typical characteristics are obtained. Then, by implementing RVM, the forecasting model for every component is developed. Finally, the forecasting results of every new component are superimposed in order to achieve the overall forecasting results with certain confidence level. Simulation results demonstrate, by comparing them with some previous methods, that the hybrid method based on EEMD-SE-RVM has relatively higher forecasting accuracy, more reliable forecasting interval and high engineering application value. Full article

Currently, in most countries, the electricity sector is liberalized, and electricity is traded in deregulated electricity markets. In these markets, electricity demand is determined the day before the physical delivery through (semi-)hourly concurrent auctions. Hence, accurate forecasts are essential for efficient and effective management of power systems. The electricity demand and prices, however, exhibit specific features, including non-constant mean and variance, calendar effects, multiple periodicities, high volatility, jumps, and so on, which complicate the forecasting problem. In this work, we compare different modeling techniques able to capture the specific dynamics of the demand time series. To this end, the electricity demand time series is divided into two major components: deterministic and stochastic. Both components are estimated using different regression and time series methods with parametric and nonparametric estimation techniques. Specifically, we use linear regression-based models (local polynomial regression models based on different types of kernel functions; tri-cubic, Gaussian, and Epanechnikov), spline function-based models (smoothing splines, regression splines), and traditional time series models (autoregressive moving average, nonparametric autoregressive, and vector autoregressive). Within the deterministic part, special attention is paid to the estimation of the yearly cycle as it was previously ignored by many authors. This work considers electricity demand data from the Nordic electricity market for the period covering 1 January 2013–31 December 2016. To assess the one-day-ahead out-of-sample forecasting accuracy, Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE) are calculated. The results suggest that the proposed component-wise estimation method is extremely effective at forecasting electricity demand. Further, vector autoregressive modeling combined with spline function-based regression gives superior performance compared with the rest. Full article

Energy commodities and their futures naturally show cointegrated price movements. However, there is empirical evidence that the prices of futures with different maturities might have, e.g., different jump behaviours in different market situations. Observing commodity futures over time, there is also evidence for different states of the underlying volatility of the futures. In this paper, we therefore allow for cointegration of the term structure within a multi-factor model, which includes seasonality, as well as joint and individual jumps in the price processes of futures with different maturities. The seasonality in this model is realized via a deterministic function, and the jumps are represented with thinned-out compound Poisson processes. The model also includes a regime-switching approach that is modelled through a Markov chain and extends the class of geometric models. We show how the model can be calibrated to empirical data and give some practical applications. Full article

Certain exotic options cannot be valued using closed-form solutions or even by numerical methods assuming constant volatility. Many exotics are priced in a local volatility framework. Pricing under local volatility has become a field of extensive research in finance, and various models are proposed in order to overcome the shortcomings of the Black-Scholes model that assumes a constant volatility. The Johannesburg Stock Exchange (JSE) lists exotic options on its Can-Do platform. Most exotic options listed on the JSE’s derivative exchanges are valued by local volatility models. These models needs a local volatility surface. Dupire derived a mapping from implied volatilities to local volatilities. The JSE uses this mapping in generating the relevant local volatility surfaces and further uses Monte Carlo and Finite Difference methods when pricing exotic options. In this document we discuss various practical issues that influence the successful construction of implied and local volatility surfaces such that pricing engines can be implemented successfully. We focus on arbitrage-free conditions and the choice of calibrating functionals. We illustrate our methodologies by studying the implied and local volatility surfaces of South African equity index and foreign exchange options. Full article