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"Stochastic Models"
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An eco-friendly closed-loop supply chain facing demand and carbon price uncertainty
The greenhouse gas emissions due to the energy use in production and distribution in a supply chain are of interest to industries aiming to achieve decarbonization. The industry subjected to carbon regulations require recycling and reusing materials to promote a circular economy through a closed-loop supply chain (CLSC). In this research, we propose a two-stage stochastic model to design the CLSC under a carbon trading scheme in the multi-period planning context by considering the uncertain demands and carbon prices. We also provide a four-step solution procedure with scenario reduction that enables the proposed model to be solved using popular commercial solvers efficiently. This solution makes the proposed model distinguished from the existing models that assume the firms can purchase or sell carbon credits without quantity limitation. The application of the proposed model is demonstrated via simulation-based analysis of the aluminum industry. The results that the proposed stochastic model generates a network with capacity redundancy to cope with the varying customer demands and carbon prices, while only a slight increase in cost and emission is observed compared with the deterministic model. Furthermore, using scenario reduction, the model solved with 80% of the scenarios share the same CLSC network configuration with the model with full scenarios, while the deviation of the total costs is less than 0.53% and the computational burden can be diminished by more than 40%. This research is expected to be useful to solve optimization problems facing large-scale scenarios with known occurrence probabilities aiming for energy conservation and emissions reduction.
Journal Article
The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well
State-of-the-art stochastic volatility models generate a \"volatility smirk\" that explains why out-of-the-money index puts have high prices relative to the Black-Scholes benchmark. These models also adequately explain how the volatility smirk moves up and down in response to changes in risk. However, the data indicate that the slope and the level of the smirk fluctuate largely independently. Although single-factor stochastic volatility models can capture the slope of the smirk, they cannot explain such largely independent fluctuations in its level and slope over time. We propose to model these movements using a two-factor stochastic volatility model. Because the factors have distinct correlations with market returns, and because the weights of the factors vary over time, the model generates stochastic correlation between volatility and stock returns. Besides providing more flexible modeling of the time variation in the smirk, the model also provides more flexible modeling of the volatility term structure. Our empirical results indicate that the model improves on the benchmark Heston stochastic volatility model by 24% in-sample and 23% out-of-sample. The better fit results from improvements in the modeling of the term structure dimension as well as the moneyness dimension.
Journal Article
Stochastic Geometry for Wireless Networks
Covering point process theory, random geometric graphs and coverage processes, this rigorous introduction to stochastic geometry will enable you to obtain powerful, general estimates and bounds of wireless network performance and make good design choices for future wireless architectures and protocols that efficiently manage interference effects. Practical engineering applications are integrated with mathematical theory, with an understanding of probability the only prerequisite. At the same time, stochastic geometry is connected to percolation theory and the theory of random geometric graphs and accompanied by a brief introduction to the R statistical computing language. Combining theory and hands-on analytical techniques with practical examples and exercises, this is a comprehensive guide to the spatial stochastic models essential for modelling and analysis of wireless network performance.
eBook
Simulating copulas : stochastic models, sampling algorithms, and applications
This tome provides the reader with a background on simulating copulas and multivariate distribution in general. It unifies the scattered literature on the simulation of various families of copulas as well as on different construction principles.
Book
Analysis of stochastic process to model safety risk in construction industry
There are many factors leading to construction safety accident. The rule presented under the influence of these factors should be a statistical random rule. To reveal those random rules and study the probability prediction method of construction safety accident, according to stochastic process theory, general stochastic process, Markov process and normal process are respectively used to simulate the risk-accident process in this paper. First, in the general-random-process-based analysis the probability of accidents in a period of time is calculated. Then, the Markov property of the construction safety risk evolution process is illustrated, and the analytical expression of probability density function of first-passage time of Markov-based risk-accident process is derived to calculate the construction safety probability. In the normal-process-based analysis, the construction safety probability formulas in cases of stationary normal risk process and non-stationary normal risk process with zero mean value are derived respectively. Finally, the number of accidents that may occur on construction site in a period is studied macroscopically based on Poisson process, and the probability distribution of time interval between adjacent accidents and the time of the nth accident are calculated respectively. The results provide useful reference for the prediction and management of construction accidents.
Journal Article
Fractional and stochastic modeling of breast cancer progression with real data validation
This study presents a novel approach to modeling breast cancer dynamics, one of the most significant health threats to women worldwide. Utilizing a piecewise mathematical framework, we incorporate both deterministic and stochastic elements of cancer progression. The model is divided into three distinct phases: (1) initial growth, characterized by a constant-order Caputo proportional operator (CPC), (2) intermediate growth, modeled by a variable-order CPC, and (3) advanced stages, capturing stochastic fluctuations in cancer cell populations using a stochastic operator. Theoretical analysis, employing fixed-point theory for the fractional-order phases and Ito calculus for the stochastic phase, establishes the existence and uniqueness of solutions. A robust numerical scheme, combining the nonstandard finite difference method for fractional models and the Euler-Maruyama method for the stochastic system, enables simulations of breast cancer progression under various scenarios. Critically, the model is validated against real breast cancer data from Saudi Arabia spanning 2004-2016. Numerical simulations accurately capture observed trends, demonstrating the model’s predictive capabilities. Further, we investigate the impact of chemotherapy and its associated cardiotoxicity, illustrating different treatment response scenarios through graphical representations. This piecewise fractional-stochastic model offers a powerful tool for understanding and predicting breast cancer dynamics, potentially informing more effective treatment strategies.
Journal Article