Search Results (99)

This paper reveals a simple methodology to create local-correlation models suitable for the closed-form pricing of two-asset financial derivatives. The multivariate models are built to ensure two conditions. First, marginals follow desirable processes, e.g., we choose the Geometric Brownian Motion (GBM), popular for stock prices. Second, the payoff of the derivative should follow a desired one-dimensional process. These conditions lead to a specific choice of the dependence structure in the form of a local-correlation model. Two popular multi-asset options are entertained: a spread option and a basket option. Full article

This study investigates a stochastic production planning problem with regime-switching parameters, inspired by economic cycles impacting production and inventory costs. The model considers types of goods and employs a Markov chain to capture probabilistic regime transitions, coupled with a multidimensional Brownian motion representing stochastic demand dynamics. The production and inventory cost optimization problem is formulated as a quadratic cost functional, with the solution characterized by a regime-dependent system of elliptic partial differential equations (PDEs). Numerical solutions to the PDE system are computed using a monotone iteration algorithm, enabling quantitative analysis. Sensitivity analysis and model risk evaluation illustrate the effects of regime-dependent volatility, holding costs, and discount factors, revealing the conservative bias of regime-switching models when compared to static alternatives. Practical implications include optimizing production strategies under fluctuating economic conditions and exploring future extensions such as correlated Brownian dynamics, non-quadratic cost functions, and geometric inventory frameworks. In contrast to earlier studies that imposed static or overly simplified regime-switching assumptions, our work presents a fully integrated framework—combining optimal control theory, a regime-dependent system of elliptic PDEs, and comprehensive numerical and sensitivity analyses—to more accurately capture the complex stochastic dynamics of production planning and thereby deliver enhanced, actionable insights for modern manufacturing environments. Full article

The article presents a new method for evaluating investment projects in uncertain conditions, assuming that uncertainty may have two origins: aleatory (related to randomness) and epistemic (due to incomplete knowledge). Epistemic uncertainty is rarely considered in investment analysis, which can result in undervaluing the future opportunities and risks. Our contribution is built around a correlated random–fuzzy Geometric Brownian Motion, a hybrid Monte Carlo engine that propagates mixed uncertainty into a probability box, combined with three p-box-to-CDF transformations (pignistic, ambiguity-based and credibility-based) to reflect decision-maker attitudes. Our approach utilizes the Datar–Mathews method (DM method) to gather relevant information regarding the potential value of a real option. By combining probabilistic and possibilistic approaches, the proposed valuation model incorporates hybrid Monte Carlo simulation and a random–fuzzy Geometric Brownian Motion, considering the interdependence between parameters. The result of the hybrid simulation is a pair of upper and lower cumulative probability distributions, known as a p-box, which represents the uncertainty range of the Net Present Value (NPV). We propose three transformations of the p-box into a subjective probability distribution, which allow decision makers to incorporate their subjective beliefs and risk preferences when performing real option valuation. Thus, our approach allows the combination of objective available information about valuation of investment with the decision maker’s attitude in front of partial ignorance. To demonstrate the effectiveness of our approach in practical scenarios, we provide a numerical illustration that clearly showcases how our approach delivers a more precise valuation of real options. Full article

The scaling up of carbon capture, utilization, and storage (CCUS) deployment is constrained by multiple factors, including technological immaturity, high capital expenditures, and extended investment return periods. The existing research on CCUS investment decisions predominantly centers on coal-fired power plants, with the utilization pathways placing a primary emphasis on storage or enhanced oil recovery (EOR). There is limited research available regarding the chemical utilization of carbon dioxide (CO₂). This study develops an options-based analytical model, employing geometric Brownian motion to characterize carbon and oil price uncertainties while incorporating the learning curve effect in carbon capture infrastructure costs. Additionally, revenues from chemical utilization and EOR are integrated into the return model. A case study is conducted on a process producing 100,000 tons of methanol annually via CO₂ hydrogenation. Based on numerical simulations, we determine the optimal investment conditions for the “CO₂-to-methanol + EOR” collaborative scheme. Parameter sensitivity analyses further evaluate how key variables—carbon pricing, oil market dynamics, targeted subsidies, and the cost of renewable electricity—influence investment timing and feasibility. The results reveal that the following: (1) Carbon pricing plays a pivotal role in influencing investment decisions related to CCUS. A stable and sufficiently high carbon price improves the economic feasibility of CCUS projects. When the initial carbon price reaches 125 CNY/t or higher, refining–chemical integrated plants are incentivized to make immediate investments. (2) Increases in oil prices also encourage CCUS investment decisions by refining–chemical integrated plants, but the effect is weaker than that of carbon prices. The model reveals that when oil prices exceed USD 134 per barrel, the investment trigger is activated, leading to earlier project implementation. (3) EOR subsidy and the initial equipment investment subsidy can promote investment and bring forward the expected exercise time of the option. Immediate investment conditions will be triggered when EOR subsidy reaches CNY 75 per barrel or more, or the subsidy coefficient reaches 0.2 or higher. (4) The levelized cost of electricity (LCOE) from photovoltaic sources is identified as a key determinant of hydrogen production economics. A sustained decline in LCOE—from CNY 0.30/kWh to 0.22/kWh, and further to 0.12/kWh or below—significantly advances the optimal investment window. When LCOE reaches CNY 0.12/kWh, the project achieves economic viability, enabling investment potentially as early as 2025. This study provides guidance and reference cases for CCUS investment decisions integrating EOR and chemical utilization in China’s refining–chemical integrated plants. Full article

This paper examines the impacts of observed versus uncertain (stochastic) institutional quality of corporate debt financing. This paper compares the impacts of two distinct levels of institutional quality in developed and developing economies. World governance indicators (WGIs) are used as proxies for institutional quality. Stochastic Geometric Brownian Motion (GBM) is used to quantify the institutional uncertainty of WGIs. The results of GLS estimates using a sample of 309 nonfinancial listed firms in G8 countries and 373 nonfinancial listed firms in MENA countries covering the years 2016–2022 show (a) positive (negative) stochastic impacts of voice and accountability (government effectiveness and political stability) on debt financing in the G8 and MENA regions; (b) although potential improvements in institutional quality are shared concerns among G8 and MENA countries, the former outperforms the latter in terms of creditors’ contract protection and enforcement, paving the way for public policy makers in the MENA region to enhance regulations that protect debt contractual obligations; (c) macroeconomic variables have sporadic impacts; GDP growth is significant in G8 but not in MENA countries; (d) the negative impacts of inflation rates are consistent in both regions; and (e) unemployment plays a negative signaling role in the G8 region only. This paper contributes to the related literature by examining the uncertain impact of institutional quality on corporate debt financing. This paper offers implications for policy makers, directing them to focus on institutional endeavors in a way that helps companies secure the debt financing required to support investment growth. Full article

This research introduces an innovative probabilistic method for examining torsional stress behavior in spherical shell structures through Monte Carlo simulation techniques. The spherical geometry of these components creates distinctive computational difficulties for conventional analytical and deterministic numerical approaches when solving torsion-related problems. The authors develop a comprehensive mesh-free Monte Carlo framework built upon the Feynman–Kac formula, which maintains the geometric symmetry of the domain while offering a probabilistic solution representation via stochastic processes on spherical surfaces. The technique models Brownian motion paths on spherical surfaces using the Euler–Maruyama numerical scheme, converting the Saint-Venant torsion equation into a problem of stochastic integration. The computational implementation utilizes the Fibonacci sphere technique for achieving uniform point placement, employs adaptive time-stepping strategies to address pole singularities, and incorporates efficient algorithms for boundary identification. This symmetry-maintaining approach circumvents the mesh generation complications inherent in finite element and finite difference techniques, which typically compromise the problem’s natural symmetry, while delivering comparable precision. Performance evaluations reveal nearly linear parallel computational scaling across up to eight processing cores with efficiency rates above 70%, making the method well-suited for multi-core computational platforms. The approach demonstrates particular effectiveness in analyzing torsional stress patterns in thin-walled spherical components under both symmetric and asymmetric boundary scenarios, where traditional grid-based methods encounter discretization and convergence difficulties. The findings offer valuable practical recommendations for material specification and structural design enhancement, especially relevant for pressure vessel and dome structure applications experiencing torsional loads. However, the probabilistic characteristics of the method create statistical uncertainty that requires cautious result interpretation, and computational expenses may surpass those of deterministic approaches for less complex geometries. Engineering analysis of the outcomes provides actionable recommendations for optimizing material utilization and maintaining structural reliability under torsional loading conditions. Full article

A model is proposed to investigate the effects of power generation source diversification and CO₂ emission control in the presence of dispatchable fossil fuel sources and non-dispatchable carbon-free renewables. In a stochastic environment in which three random factors are considered, namely fossil fuels (gas and coal) and CO₂ prices, we discuss a planning methodology for power system portfolio selection that integrates the non-dispatchable renewables available in a given energy system and optimally combines cost, risk and CO₂ emissions. By combining the deep neural network probabilistic forecasting of fossil fuel path prices with a geometric Brownian motion model for describing the CO₂ price dynamics, we simulate a wide range of plausible market scenarios. Results show that under CO₂ price volatility, optimal portfolios shift toward cleaner energy sources, even in the absence of explicit emission targets, highlighting the implicit regulatory power of volatility. The results suggest that incorporating CO₂ price volatility through market mechanisms can serve as an effective policy tool for driving decarbonization. Our model offers a flexible and reproducible approach to support policy design in energy planning under uncertainty. Full article

In order to realize green and low-carbon transformation, some ports have explored the path of sustainable equipment upgrading by adjusting the energy structure of yard cranes in recent years. However, there are multiple uncertainties in the investment process of hydrogen-powered yard cranes, and the existing valuation methods fail to effectively deal with these dynamic changes and lack scientifically sound decision support tools. To address this problem, this study constructs a multi-factor real options model that integrates the dynamic uncertainties of hydrogen price, carbon price, and technology maturity. In this study, a geometric Brownian motion is used for hydrogen price simulation, a Markov chain model with jump diffusion term and stochastic volatility is used for carbon price simulation, and a learning curve method is used to quantify the evolution of technology maturity. Aiming at the long investment cycle of ports, a hybrid option strategy of “American and European” is designed, and the timing and scale of investment are dynamically optimized by Monte Carlo simulation and least squares regression. Based on the empirical analysis of Qingdao Port, the results show that the optimal investment plan for hydrogen-powered yard cranes project under the framework of a multi-factor option model is to use an American-type option to maintain moderate flexibility in the early stage, and to use a European-type option to lock in the return in the later stage. The study provides decision support for the green development of ports and enhances economic returns and carbon emission reduction benefits. Full article

This paper is dedicated to studying the optimal investment proportions of three types of assets with symmetry, namely, risky assets, risk-free assets, and wealth management products, when the stochastic expenditure process follows a jump-diffusion model. The stochastic expenditure process is treated as an exogenous cash flow and is assumed to follow a stochastic differential process with jumps. Under the Cox–Ingersoll–Ross interest rate term structure, it is presumed that the prices of multiple risky assets evolve according to a multi-dimensional geometric Brownian motion. By employing stochastic control theory, the Hamilton–Jacobi–Bellman (HJB) equation for the household portfolio problem is formulated. Considering various risk-preference functions, particularly the Hyperbolic Absolute Risk Aversion (HARA) function, and given the algebraic form of the objective function through the terminal-value maximization condition, an explicit solution for the optimal investment strategy is derived. The findings indicate that when household investment behavior is characterized by random expenditures and symmetry, as the risk-free interest rate rises, the optimal proportion of investment in wealth-management products also increases, whereas the proportion of investment in risky assets continually declines. As the expected future expenditure increases, households will decrease their acquisition of risky assets, and the proportion of risky-asset purchases is sensitive to changes in the expectation of unexpected expenditures. Full article

Efficient management of bankruptcy risk requires treating distant-to-default (DD) stochastically as long as historical stock prices move randomly and, thus, do not guarantee that history may repeat itself. Using long-term data that date back to 1952–2023, including the nonfinancial companies listed in the Dow Jones Industrial Average and National Association of Securities Dealers Automated Quotations indexes, this study estimates the historical and stochastic DDs via the geometric Brownian motion (GBM). The results show that (a) the association between the debt-to-equity ratio and the stochastic DD can be used as an indicator of excessive debt financing; (b) debt tax savings have a positive effect on stochastic DD; (c) bankruptcy costs have negative effects on stochastic DD; (d) in terms of the size of the company being proxied by sales revenue and the equity market value of the company, the DD is a reliable measure of bankruptcy costs; (e) in terms of macroeconomic influences, increases in the percentage change in manufacturing output are associated with lower observed and stochastic DD; and (f) in terms of the influences of industry, the stochastic DD is affected by the industry average retail inventory to sales. This paper contributes to related studies in terms of focusing on the indicators that a company’s management can focus on to address the stochastic patterns inherent in the estimation of the DD. Full article

Based on allometric theory and scaling laws, numerous mathematical models have been proposed to study ontogenetic growth patterns of animals. Although deterministic models have provided valuable insight into growth dynamics, animal growth often deviates from strict deterministic patterns due to stochastic factors such as genetic variation and environmental fluctuations. In this study, we extend a general model for ontogenetic growth proposed by West et al. to stochastic models for ontogenetic growth by incorporating stochasticity using white noise. According to data variance fitting for stochasticity, we propose two stochastic models for ontogenetic growth, one is for determinate growth and one is for indeterminate growth. To develop a universal stochastic process for ontogenetic growth across diverse species, we approximate stochastic trajectories of two stochastic models, apply random time change, and obtain a geometric Brownian motion with a multiplier of an exponential time factor. We conduct detailed mathematical analysis and numerical analysis for our stochastic models. Our stochastic models not only predict average growth well but also variations in growth within species. This stochastic framework may be extended to studies of other growth phenomena. Full article

We address the problem of asset pricing in a market where there are no risky assets. Previous work developed a theoretical model for a shadow riskless rate (SRR) for such a market, based on the drift component of the state-price deflator for that asset universe. Assuming that asset prices are modeled by correlated geometric Brownian motion, in this work, we develop a computational approach to estimate the SRR from empirical datasets. The approach employs principal component analysis to model the effects of individual Brownian motions, singular value decomposition to capture abrupt changes in the condition number of the linear system whose solution provides the SRR values, and regularization to control the rate of change of the condition number. Among other uses such as option pricing and developing a term structure of interest rates, the SRR can be used as an investment discriminator between different asset classes. We apply this computational procedure to markets consisting of various groups of stocks, encompassing different asset types and numbers. The theoretical and computational analysis provides the drift as well as the total volatility of the state-price deflator. We investigate the time trajectory of these two descriptive components of the state-price deflator for the empirical datasets. Full article

This paper proposes and implements a methodology to fit a seven-parameter Generalized Tempered Stable (GTS) distribution to financial data. The nonexistence of the mathematical expression of the GTS probability density function makes maximum-likelihood estimation (MLE) inadequate for providing parameter estimations. Based on the function characteristic and the fractional Fourier transform (FRFT), we provide a comprehensive approach to circumvent the problem and yield a good parameter estimation of the GTS probability. The methodology was applied to fit two heavy-tailed data (Bitcoin and Ethereum returns) and two peaked data (S&P 500 and SPY ETF returns). For each historical data, the estimation results show that six-parameter estimations are statistically significant except for the local parameter, $\mu$. The goodness of fit was assessed through Kolmogorov–Smirnov, Anderson–Darling, and Pearson’s chi-squared statistics. While the two-parameter geometric Brownian motion (GBM) hypothesis is always rejected, the GTS distribution fits significantly with a very high p-value and outperforms the Kobol, Carr–Geman–Madan–Yor, and bilateral Gamma distributions. Full article

Poisson regression is a statistical method specifically designed for analyzing count data. Considering the case where the functional and vector-valued covariates exhibit a linear relationship with the log-transformed Poisson mean, while the covariates in complex domains act as nonlinear random effects, an intrinsic functional partially linear Poisson regression model is proposed. This model flexibly integrates predictors from different spaces, including functional covariates, vector-valued covariates, and other non-Euclidean covariates taking values in complex domains. A truncation scheme is applied to approximate the functional covariates, and the random effects related to non-Euclidean covariates are modeled based on the reproducing kernel method. A quasi-Newton iterative algorithm is employed to optimize the parameters of the proposed model. Furthermore, to capture the intrinsic geometric structure of the covariates in complex domains, the heat kernel is employed as the kernel function, estimated via Brownian motion simulations. Both simulation studies and real data analysis demonstrate that the proposed method offers significant advantages over the classical Poisson regression model. Full article

This paper proposes a deep neural network (DNN) model to estimate the Hurst exponent, a crucial parameter in modelling stock market price movements driven by fractional geometric Brownian motion. We randomly selected 446 indices from the S&P 500 and extracted their price movements over the last 2010 trading days. Using the rescaled range (R/S) analysis and the detrended fluctuation analysis (DFA), we computed the Hurst exponent and related parameters, which serve as the target parameters in the DNN architecture. The DNN model demonstrated remarkable learning capabilities, making accurate predictions even with small sample sizes. This addresses a limitation of R/S analysis, known for biased estimates in such instances. The significance of this model lies in its ability, once trained, to rapidly estimate the Hurst exponent, providing results in a small fraction of a second. Full article