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We present an approach for pricing American put options with a regime-switching volatility. Our method reveals that the option price can be expressed as the sum of two components: the price of a European put option and the premium associated with the early exercise privilege. Our analysis demonstrates that, under these conditions, the perpetual put option consistently commands a higher price during periods of high volatility compared to those of low volatility. Moreover, we establish that the optimal exercise boundary is lower in high-volatility regimes than in low-volatility regimes. Additionally, we develop an analytical framework to describe American puts with an Erlang-distributed random-time horizon, which allows us to propose a numerical technique for approximating the value of American puts with finite expiry. We also show that a combined approach involving randomization and Richardson extrapolation can be a robust numerical algorithm for estimating American put prices with finite expiry.

In this study, the authors propose a novel digital twinning approach specifically designed for controlling transient thermal systems. The purpose of this study is to harness the combined power of deep learning (DL) and physics-based methods (PBM) to create an active virtual replica of the physical system.

To achieve this goal, we introduce a deep neural network (DNN) as the digital twin and a Finite Element (FE) model as the physical system. This integrated approach is used to address the challenges of controlling an unsteady heat transfer problem with an integrated feedback loop.

The results of our study demonstrate the effectiveness of the proposed digital twinning approach in regulating the maximum temperature within the system under varying and unsteady heat flux conditions. The DNN, trained on stationary data, plays a crucial role in determining the heat transfer coefficients necessary to maintain temperatures below a defined threshold value, such as the material’s melting point. The system is successfully controlled in 1D, 2D and 3D case studies. However, careful evaluations should be conducted if such a training approach, based on steady-state data, is applied to completely different transient heat transfer problems.

The present work represents one of the first examples of a comprehensive digital twinning approach to transient thermal systems, driven by data. One of the noteworthy features of this approach is its robustness. Adopting a training based on dimensionless data, the approach can seamlessly accommodate changes in thermal capacity and thermal conductivity without the need for retraining.

The safety and reliability of high-speed trains rely on the structural integrity of their components and the dynamic performance of the entire vehicle system. This paper aims to define and substantiate the assessment of the structural integrity and dynamical integrity of high-speed trains in both theory and practice. The key principles and approaches will be proposed, and their applications to high-speed trains in China will be presented.

First, the structural integrity and dynamical integrity of high-speed trains are defined, and their relationship is introduced. Then, the principles for assessing the structural integrity of structural and dynamical components are presented and practical examples of gearboxes and dampers are provided. Finally, the principles and approaches for assessing the dynamical integrity of high-speed trains are presented and a novel operational assessment method is further presented.

Vehicle system dynamics is the core of the proposed framework that provides the loads and vibrations on train components and the dynamic performance of the entire vehicle system. For assessing the structural integrity of structural components, an open-loop analysis considering both normal and abnormal vehicle conditions is needed. For assessing the structural integrity of dynamical components, a closed-loop analysis involving the influence of wear and degradation on vehicle system dynamics is needed. The analysis of vehicle system dynamics should follow the principles of complete objects, conditions and indices. Numerical, experimental and operational approaches should be combined to achieve effective assessments.

The practical applications demonstrate that assessing the structural integrity and dynamical integrity of high-speed trains can support better control of critical defects, better lifespan management of train components and better maintenance decision-making for high-speed trains.

This paper presents an experimental investigation in establishing the relationship between FDM process parameters and tensile strength of polycarbonate (PC) samples using the I-Optimal design.

I-optimal design methodology is used to plan the experiments by means of Minitab-17.1 software. Samples are manufactured using Stratsys FDM 400mc and tested as per ISO standards. Additionally, an artificial neural network model was developed and compared to the regression model in order to select an appropriate model for optimisation. Finally, the genetic algorithm (GA) solver is executed for improvement of tensile strength of FDM built PC components.

This study demonstrates that the selected process parameters (raster angle, raster to raster air gap, build orientation about Y axis and the number of contours) had significant effect on tensile strength with raster angle being the most influential factor. Increasing the build orientation about Y axis produced specimens with compact structures that resulted in improved fracture resistance.

The fitted regression model has a p-value less than 0.05 which suggests that the model terms significantly represent the tensile strength of PC samples. Further, from the normal probability plot it was found that the residuals follow a straight line, thus the developed model provides adequate predictions. Furthermore, from the validation runs, a close agreement between the predicted and actual values was seen along the reference line which further supports satisfactory model predictions.

This study successfully investigated the effects of the selected process parameters - raster angle, raster to raster air gap, build orientation about Y axis and the number of contours - on tensile strength of PC samples utilising the I-optimal design and ANOVA. In addition, for prediction of the part strength, regression and ANN models were developed. The selected ANN model was optimised using the GA-solver for determination of optimal parameter settings.

The proposed ANN-GA approach is more appropriate to establish the non-linear relationship between the selected process parameters and tensile strength. Further, the proposed ANN-GA methodology can assist in manufacture of various industrial products with Nylon, polyethylene terephthalate glycol (PETG) and PET as new 3DP materials.

Our result of this paper aims to indicate that the beta pricing formula could be applied in a long-term model setting as well.

In this paper, we show that the capital asset pricing model can be derived from a three-period general equilibrium model.

We show that our extended model yields a Pareto efficient outcome.

The capital asset pricing model (CAPM) model can be used for pricing long-lived assets.

Long-term modelling and sustainability can be modelled in our setting.

Our results were only known for two periods. The extension to 3 periods opens up a large scope of applicational possibilities in asset pricing, behavioural analysis and long-term efficiency.