Stochastic Factors Research Articles

Dynamic pricing strategies for efficient inventory management with auto-correlative stochastic demand forecasting using exponential smoothing method

The research presents a novel approach to inventory modelling, emphasizing stochastic demand and dynamic pricing strategies for a seasonal sales framework. The methodology divides the sales season into intervals, each associated with distinct pricing strategies influenced by stochastic factors. The study employ exponential smoothing for demand forecasting, optimizing inventory replenishment and dynamic pricing strategies through developed algorithms. Notably, the study determine the optimal smoothing parameter for demand forecasting, balancing responsiveness to recent demand patterns with long-term stability. Proposed research achieves a comprehensive framework empowering businesses to enhance competitiveness and profitability by addressing challenges of stochastic demand and dynamic pricing. Dynamic pricing strategies outperformed classical strategies, allowing businesses to respond promptly to demand fluctuations and optimize profit margins during sales seasons. Incorporating stochastic demand models enabled organizations to implement safety stock and buffer inventory levels effectively, mitigating risks associated with uncertain demand patterns. Real-time data analysis was crucial for adjusting price dynamics and making effective management decisions, leading to improved financial performance. The iterative nature of dynamic pricing strategies emphasized the importance of continuous refinement to adapt to evolving market dynamics. This approach enables data-driven decisions, adaptation to market fluctuations, and improved inventory management despite unpredictable demand. Ultimately, this study provides valuable insights and methodologies applicable across industries for efficient and profitable inventory management.

Impacts of oxbow lake evolution on sediment microbial community structure in the Yellow River source region

Oxbow lake formation and evolution have significant impacts on the fragile Yellow River Basin ecosystem. However, the effects of different oxbow lake evolutionary stages on sediment microbial community structure are not yet understood comprehensively. Therefore, microbial community structure in three stages of oxbow lake succession, namely, lotic lake (early stage), semi-lotic lake (middle stage), and lentic lake (late stage), was investigated in the present study in the Yellow River Basin on the Qinghai-Tibet Plateau. Amplicon sequencing was employed to reveal differences in microbial community diversity and composition. The bacterial and fungal communities in sediment were significantly different among the three succession stages and were driven by different environmental factors. In particular, bacterial community structure was influenced primarily by nitrate-nitrogen (N), microbial biomass phosphorus, and total carbon (C) and organic C in the early, middle, and late stages, respectively. Conversely, fungal community structure was influenced primarily by ammonium-N in the early stage and by moisture content in the middle and late stages. However, the predicted functions of the microbial communities did not exhibit significant differences across the three succession stages. Both bacteria and fungi were influenced significantly by stochastic factors. Homogeneous selection had a high relative contribution to bacteria community assembly in the middle stage, whereas the relative contributions of heterogeneous selection processes to fungal community assembly increased through the three stages. As succession time increased, the total number of keystone species increased gradually, and the late succession stage had high network complexity and the highest network stability. The findings could facilitate further elucidation of the evolution mechanisms of oxbow lake source area, high-altitude river evolution dynamics, in addition to aiding a deeper understanding of the long-term ecological evolution patterns of source river ecosystems.

Dynamic characteristics of expectations of short-term interest rate and a generalized Vasicek model

This study's principal mathematical deduction exploits the importance of the specification of long-term equilibrium level in the mean-reversion short-term interest rate model—such as the CKLS (Chan, Karolyi, Longstaff, and Sanders) model—to describe the dynamic characteristics of future short-term interest rate expectations, especially long-horizon expectations. Therefore, we present a preferred model by introducing a stochastic long-run equilibrium level factor to extend the specifications of the Vasicek model's short-term interest rate dynamics. Using this new type of short-term interest rate as a driver we develop a two-factor affine arbitrage-free model of term structure, the generalized Vasicek mode. The empirical results show that the model not only has a good sample fitting ability to the Chinese government bond yield curve, but also has better performance in capturing the dynamic characteristics of short-term interest rates and short-term interest rate expectations. This study provides not only a promising avenue for future research on improving interest rate modeling techniques and their practical applications in the financial industry but also a new literature base for accurately identifying public expectations and explaining the underlying mechanisms of expectation changes.

Spatial and temporal variation and convergence in the efficiency of high-standard farmland construction: Evidence in China

To assess the efficiency of high-standard farmland construction (HSFC), this study utilized data spanning from 1998 to 2020 obtained from 30 provinces, autonomous regions, and municipalities in China. This assessment was conducted using a three-stage super-efficient slack-based measure data envelopment analysis(SBM-DEA)model. Furthermore, we investigated the spatial and temporal variances and convergence of HSFC efficiency using the Dagum Gini coefficient and convergence analysis. The results firstly show that from 2007 to 2020, China's HSFC efficiency displayed fluctuations and declines, significantly influenced by environmental and stochastic factors. Secondly, it showed that the gap in China's HSFC efficiency has widened, with super-variable density being demonstrated as the primary source of spatial imbalance in HSFC efficiency. Thirdly, it showed that the deviation in the efficiency of HSFC in the central region of China from the average level has shown a gradually declining trend, while the deviation in the efficiency of HSFC in the national, western, eastern, and northeastern regions has not presented a downward trend. Fourthly, it demonstrated that over time, the efficiency of building high-standard agriculture throughout the nation and its four main areas will converge to the same level.

Bacterial and fungal community structures in Hulun Lake are regulated by both stochastic processes and environmental factors.

Microorganisms are a crucial component of lake ecosystems and significant contributors to biogeochemical cycles. However, the understanding of how primary microorganism groups (e.g., bacteria and fungi) are distributed and constructed within different lake habitats is lacking. We investigated the bacterial and fungal communities of Hulun Lake using high-throughput sequencing techniques targeting 16S rRNA and Internal Transcribed Spacer 2 genes, including a range of ecological and statistical methodologies. Our findings reveal that environmental factors have high spatial and temporal variability. The composition and community structures vary significantly depending on differences in habitats. Variance partitioning analysis showed that environmental and geographical factors accounted for <20% of the community variation. Canonical correlation analysis showed that among the environmental factors, temperature, pH, and dissolved oxygen had strong control over microbial communities. However, the microbial communities (bacterial and fungal) were primarily controlled by the dispersal limitations of stochastic processes. This study offers fresh perspectives regarding the maintenance mechanism of bacterial and fungal biodiversity in lake ecosystems, especially regarding the responses of microbial communities under identical environmental stress.IMPORTANCELake ecosystems are an important part of the freshwater ecosystem. Lake microorganisms play an important role in material circulation and energy flow owing to their unique enzymatic and metabolic capacity. In this study, we observed that bacterial and fungal communities varied widely in the water and sediments of Hulun Lake. The primary factor affecting their formation was identified as dispersal limitation during stochastic processes. Environmental and geographical factors accounted for <20% of the variation in bacterial and fungal communities, with pH, temperature, and dissolved oxygen being important environmental factors. Our findings provide new insights into the responses of bacteria and fungi to the environment, shed light on the ecological processes of community building, and deepen our understanding of lake ecosystems. The results of this study provide a reference for lake management and conservation, particularly with respect to monitoring and understanding microbial communities in response to environmental changes.

Data‐driven out‐of‐order model for synchronized planning, scheduling, and execution in modular construction fit‐out management

AbstractFit‐out operations in modular construction exhibit unique features, such as limited room space and diversely distributed operations in the building. These features pose significant challenges to planning, scheduling, and execution (PSE) of fit‐out activities due to operational parallelism, distributional diversity, and narrower constrained time window in modular construction. Hence, logistics‐operation and multi‐operations synchronizations in a real‐time manner are crucial for PSE of modular construction fit‐out management. With the support of cutting‐edge information technologies, the real‐time data inside the generated digital twins can simplify online optimization models and convert stochastic factors into deterministic parameters. This paper formulates a novel real‐time data‐driven Out‐of‐Order (OoO) model for synchronized PSE in modular construction fit‐out management. Drawing inspiration from OoO mechanism in Central Processing Unit (CPU), a real‐time data‐driven and rolling‐horizon‐based OoO model is proposed for PSE of modular construction fit‐out, employing a forward heuristic algorithm for solution. Time–space–state data from digital twins are updated to facilitate dynamic decision‐making of managers. Through stochastic computational experiments, we demonstrate the effectiveness of OoO model in optimizing project metrics and the improved resilience in uncertain environments.

Enhanced Dung Beetle Optimization Algorithm for Practical Engineering Optimization

An enhanced dung beetle optimization algorithm (EDBO) is proposed for nonlinear optimization problems with multiple constraints in manufacturing. Firstly, the dung beetle rolling phase is improved by removing the worst value interference and coupling the current solution with the optimal solution to each other, while retaining the advantages of the original formulation. Subsequently, to address the problem that the dung beetle dancing phase focuses only on the information of the current solution, which leads to the overly stochastic and inefficient exploration of the problem space, the globally optimal solution is introduced to steer the dung beetle, and a stochastic factor is added to the optimal solution. Finally, the dung beetle foraging phase introduces the Jacobi curve to further enhance the algorithm’s ability to jump out of the local optimum and avoid the phenomenon of premature convergence. The performance of EDBO in optimization is tested using the CEC2017 function set, and the significance of the algorithm is verified by the Wilcoxon rank-sum test and the Friedman test. The experimental results show that EDBO has strong optimization-seeking accuracy and optimization-seeking stability. By solving four engineering optimization problems of varying degrees, EDBO has proven to have good adaptability and robustness.

STEWART PLATFORM DYNAMICS MODEL IDENTIFICATION

Context. At the present stage, with the current demands for the accuracy of motion control processes for a moving object on a specified or programmable trajectory, it is necessary to synthesize the optimal structure and parameters of the stabilization system (controller) of the object, taking into account both real controlled and uncontrolled stochastic disturbing factors. Also, in the process of synthesizing the optimal controller structure, it is necessary to assess and consider multidimensional dynamic models, including those of the object itself, its basic components, controlled and uncontrolled disturbing factors that affect the object in its actual motion.&#x0D; Objective. The aim of the research, the results of which are presented in this article, is to obtain and assess the accuracy of the Stewart platform dynamic model using a justified algorithm for the multidimensional moving object dynamics identification.&#x0D; Method. The article employs a frequency-domain identification method for multidimensional stochastic stabilization systems of moving objects with arbitrary dynamics. The proposed algorithm for multidimensional moving object dynamics model identification is constructed using operations of polynomial and fractional-rational matrices addition, multiplication, Wiener factorization, Wiener separation, and determination of dispersion integrals.&#x0D; Results. As a result of the conducted research, the problem of identifying the dynamic model of a multidimensional moving object is formalized, illustrated by the example of a test stand based on the Stewart platform. The outcomes encompass the identification of the dynamic model of the Stewart platform, its transfer function, and the transfer function of the shaping filter. The verification of the identification results confirms the sufficient accuracy of the obtained models.&#x0D; Conclusions. The justified identification algorithm allows determining the order and parameters of the linearized system of ordinary differential equations for a multidimensional object and the matrix of spectral densities of disturbances acting on it under operating conditions approximating the real functioning mode of the object prototype. The analysis of the identification results of the dynamic models of the Stewart platform indicates that the primary influence on the displacement of the center of mass of the moving platform is the variation in control inputs. However, neglecting the impact of disturbances reduces the accuracy of platform positioning. Therefore, for the synthesis of the control system, methods should be applied that enable determining the structure and parameters of a multidimensional controller, considering such influences.

Finite-Time Adaptive Fuzzy Backstepping Control for Quadrotor UAV With Stochastic Disturbance

This paper proposes an adaptive fuzzy output feedback control approach for quadrotor unmanned aerial vehicles (QUAV) with stochastic disturbances, besides which we consider the unmeasurable states and unknown nonlinear functions. The QUAV system contains stochastic terms which are not bounded and not differentiable. By combining the It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\hat{\rm \textbf{o}}$</tex-math> </inline-formula> differential equation with finite-time theory, a novel stochastic finite-time stability controller for QUAV is raised for the first time. The fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions in the model. Dynamic surface control technology is introduced to reduce the complexity of differential. Furthermore, an observer with FLS is designed through the adaptive backstepping technique to estimate the immeasurable states. It is proved that this control approach can ensure that all states of the closed-loop QUAV system are semi-global and finite-time stable in probability. Meanwhile, the errors of system outputs and observer converge to a small neighborhood of origin. The simulation results show the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In practical applications, many systems are often affected by internal and external disturbances, and not all of them can be described by mathematical models, so they are called stochastic disturbances. Taking the QUAV as an example, when the system is disturbed by internal parameters, external environment, system input, sensor error, and other stochastic factors, the deterministic system can no longer accurately describe the controlled object. In this paper, the QUAV is regarded as a stochastic system for the first time, and a novel controller is designed to solve the above problems. In addition, the QUAV needs fast action in some applications, such as emergency collision avoidance, which has high requirements for the convergence performance of the controller. Therefore, studying the finite-time control for QUAV systems with stochastic disturbances is necessary. At the same time, this paper also considers the problem that the state is not measurable and the system contains unknown nonlinear equations.

ANALYTICALLY PRICING EUROPEAN OPTIONS UNDER A TWO-FACTOR STOCHASTIC INTEREST RATE MODEL WITH A STOCHASTIC LONG-RUN EQUILIBRIUM LEVEL

AbstractWe construct a new stochastic interest rate model with two stochastic factors, by introducing a stochastic long-run equilibrium level into the Vasicek interest rate model which follows another Ornstein–Uhlenbeck process. With the interest rate under the Black–Scholes model being assumed to follow the newly proposed model, a closed-form representation of European option prices is successfully presented, when the analytical characteristic function of the underlying log-price under a forward measure is derived. To assess the model performance, a preliminary empirical study is conducted using S&amp;P 500 index and its options, with the Vasicek model and an alternative two-factor Vasicek model taken as benchmarks.

Effective vaccination strategies for human papillomavirus (HPV) infection and cervical cancer based on the mathematical model with a stochastic process.

Human papillomavirus (HPV) infection poses a significant risk to women's health by causing cervical cancer. In addition to HPV, cervical cancer incidence rates can be influenced by various factors, including human immunodeficiency virus and herpes, as well as screening policy. In this study, a mathematical model with stochastic processes was developed to analyze HPV transmission between genders and its subsequent impact on cervical cancer incidence. The model simulations suggest that both-gender vaccination is far more effective than female-only vaccination in preventing an increase in cervical cancer incidence. With increasing stochasticity, the difference between the number of patients in the vaccinated group and the number in the nonvaccinated group diminishes. To distinguish the patient population distribution of the vaccinated from the nonvaccinated, we calculated effect size (Cohen's distance) in addition to Student's t-test. The model analysis suggests a threshold vaccination rate for both genders for a clear reduction of cancer incidence when significant stochastic factors are present.

A novel SCNN-LSTM model for predicting the SNR confidence interval in wearable wireless sensor network

Accurate real-time prediction of link quality is crucial for enhancing the reliable responsiveness of wearable devices within Wireless Wearable Sensor Networks (WWSNs). Specifically, the Signal-to-Noise Ratio (SNR), a pivotal parameter for predicting link quality, exhibits complex temporal characteristics influenced by stochastic and non-stochastic factors. To improve the accuracy of link quality prediction in WWSNs, we aim to explore a novel predictive model, introducing a filtering layer that seeks to enhance the precision of predicting upper and lower boundaries of link reliability confidence intervals. First, we adopt the SNR time series as the evaluation metric and decompose the SNR sequences into time-varying and stochastic standard deviation sequences by wavelet decomposition. Subsequently, we propose an innovative SCNN-LSTM model, incorporating the SincNet filtering layer to extract specific frequency components from the input SNR sequences. Afterward, integrating standard deviation sequences, the model predicts upper and lower boundaries of link reliability confidence intervals. Finally, we conduct the validation experiments on the public dataset LightGBM-LQP and our WWSN dataset Basketball shot. Compared to BPNN, ARIMA, and WNN, the evaluation matrices of MAE, RMSE, R2 in SCNN-LSTM have been improved, and the deviation between the predicted standard deviation and the actual standard deviation has reached the minimum of 0.1. The results demonstrate that SCNN-LSTM outperforms classical prediction models in predicting upper and lower limits of link reliability confidence intervals in WWSNs.

Evolution analysis of low-carbon cooperation of service providers based on Moran process in cloud manufacturing.

Low-carbon cooperation among cloud manufacturing service providers is one way to achieve carbon peak and neutrality. Such cooperation is related to the benefits to service providers adopting low-carbon strategies and stochastic factors such as government low-carbon policies, providers' environmental awareness, and demanders' low-carbon preferences. Focusing on the evolutionary process of service providers' low-carbon strategy selection under uncertain factors, a stochastic evolutionary game model is constructed based on the Moran process, and the equilibrium conditions for low-carbon cooperation among providers are analyzed under benefit-dominated and stochastic factor-dominated situations. Through numerical simulation, the effects of the cloud platform's cost-sharing coefficient for low-carbon investment, matching growth rate, carbon trading price, and group size on providers' low-carbon strategy evolution are analyzed. The research results show that increasing the cloud platform's low-carbon cost-sharing, carbon trading price, and group size can promote low-carbon cooperation among service providers. With greater low-carbon investment costs and greater stochastic factor interference, the providers' enthusiasm for low-carbon cooperation decreases. This study fills the research gap in the low-carbon cooperation evolution of cloud manufacturing providers based on the stochastic evolutionary game and provides decision-making suggestions for governments and cloud platforms to encourage provider participation in low-carbon cooperation and for providers to adopt low-carbon strategies.

Spectral analysis of solar-irradiance fluctuations

Solar-irradiance fluctuations possess a power-law spectrum with two different slopes in the intermediate (1/day &lt;f&lt;1/h) and high [1/h &lt;f&lt;1/(2 min)] frequency (f) regimes. This spectrum is a combination of a deterministic (latitude-dependent) variation of daylight duration and a stochastic component arising from various environmental attenuation factors. We propose a principled approach to decompose the solar-irradiance time series into the deterministic location-dependent clear sky and the stochastic environmental attenuation signals. Such decomposition permits one to systematically analyze the solar photovoltaic power-fluctuation spectra after accounting for the strong geographic dependence, failing which no baseline standard exists with which to compare spectra between disparate geographic locations. Our analysis for two different locations shows that the stochastic environmental factors determine the spectral power-law slope in the high-frequency range, while the deterministic clear-sky signal plays a role in the intermediate frequency range. We close by discussing its implications for solar photovoltaic power production, in particular, for the geographic smoothing of fluctuations. Published by the American Physical Society 2024

EFFICIENT WRONG-WAY RISK MODELING FOR FUNDING VALUATION ADJUSTMENTS

Wrong-Way Risk (WWR) is an important component in Funding Valuation Adjustment (FVA) modeling. Yet, the standard assumption is independence between market risks and the counterparty defaults and funding costs. This typical industrial setting is our point of departure, where we aim to assess the impact of WWR without running a full Monte Carlo simulation with all credit and funding processes. We propose to split the exposure profile into two parts: an independent and a WWR-driven part. For the former, exposures can be re-used from the standard xVA calculation. We express the second part of the exposure profile in terms of the stochastic drivers and approximate these by a common Gaussian stochastic factor. Within the affine setting, the proposed approximation is generic, is an add-on to the existing xVA calculations and provides an efficient and robust way to include WWR in FVA modeling. Case studies for an interest rate swap and a representative multi-currency portfolio of swaps illustrate that the approximation method is applicable in a practical setting. We analyze the approximation error and use the approximation to compute WWR sensitivities, which are needed for risk management. The approach is equally applicable to other metrics such as Credit Valuation Adjustment.

Detection of long-term land use and ecosystem services dynamics in the Loess Hilly-Gully region based on artificial intelligence and multiple models

Balancing intensive development with biodiversity conservation is critical for ecological sustainability. In the Loess Hilly-Gully region, which has experienced significant environmental changes from 1980 to 2020, land use changes are vital for ecosystem service maintenance. However, these processes are susceptible to environmental stressors such as climate change, land degradation, and inadequate land management. Despite recognizing these stressors, their combined impact on land use and ecosystem services is not well understood. This study addresses this gap by utilizing multi-model land use simulations combined with artificial intelligence to analyze changes over the four-decade period. We focused on identifying ecological nodes essential for landscape connectivity, finding that these nodes significantly enhance regional ecosystem services. We also examined the relationship between land use changes and ecosystem services under various environmental stressors within the specified timeframe. Our analysis indicates that land use changes are a strong indicator of ecosystem evolution in these areas. We observed that under natural conditions, land use and ecosystem services interactions are governed by both stochastic and deterministic factors. Interestingly, multiple stressors intensified the stochastic nature of land use changes and the deterministic aspects of ecosystem services. Specifically, climate change, coupled with suboptimal land management, significantly affects this relationship, with climate change being the most influential factor on land use patterns during the studied period. This research offers important insights for improved environmental management and reducing impacts on aquatic ecosystems amid escalating climate change threats.

Ecological role of reed belts in lakeside zone: Impacts on nutrient retention and bacterial community assembly during Hydrilla verticillata decomposition

Reed belts acting as basic nutrient filters are important parts of lake buffer riparian zones. However, little is known about their impacts on nutrient release and bacterial community during plant litter decomposition. In this study, a field experiment was conducted in west-lake Taihu to monitor the changes in nutrients, bacterial enzymatic activities, and bacterial community in plant debris during Hydrilla verticillata (H. verticillata) decomposition in open water (HvC) and reed belts (HvL) area for 126 days. We found that there was lower temperature but higher nutrient concentrations in overlying water in HvL than HvC. Partial least squares path modeling revealed that environmental parameters in overlying water had important impacts on bacterial activities and nutrient release (such as alkaline phosphatase, cellulase, and soluble sugar) and therefore affected dissolved organic matter components in plant debris. According to Illumina sequencing, 46,003 OTUs from 10 dominant phyla were obtained and Shannon index was higher in HvL than HvC at the same sampling time. Neutral community model explained 49% of bacterial community variance and immigration rate by the estimate of dispersal in HvC (Nm: 27,154) and HvL (Nm: 25,765), respectively. Null model showed stochastic factors governed the bacterial community assembly in HvC (66.67%) and HvL (87.28%). TP and pH were key factors affecting the bacterial community structure at the phylum level. More hubs and complex interactions among bacteria were observed in HvL than HvC. Function analysis showed bacterial community had important role in carbon, organic phosphorus, and nitrogen removal but phosphorus-starvation was detected in debris of H. verticillata. This study provides useful information for understanding the changes in nutrients and bacterial community in litter during H. verticillata decomposition and highlights the role of reed belts on retained plant litter to protect lake from pollution.

A novel epidemiologically informed particle filter for assessing epidemic phenomena. Application to the monkeypox outbreak of 2022

Contagious diseases are constantly affecting more and more people every day, resulting in widespread health crises especially in developing nations. Previous studies have developed deterministic and stochastic mathematical models to investigate the spread of epidemics. In the present study, a hybrid particle filtering epidemiological model is proposed, which combines the elements of a deterministic susceptible-exposed-infectious-recovered-deceased model with the inclusion of stochastic and penalty factors, in order to efficiently evaluate the dynamics of the disease. The inclusion of penalty factors stands out as the main novelty of the proposed methodology, guaranteeing estimations that align with the unique aspects of the examined natural phenomenon. The model is applied to the monkeypox data of the United States from 25 June to 21 November 2022. Our approach is compared to four alternatives, corresponding to deterministic and stochastic approaches that are associated with either fixed or time-varying parameters. In all cases, the particle filtering models displayed better characteristics in terms of infectious cases and deaths compared to their deterministic counterpart. The final version of the proposed epidemiologically informed particle filtering model exhibited significant potential and provided the best fitting/predictive performance compared to other examined methodologies. The predictive effectiveness of the proposed methodology has been thoroughly evaluated across various time intervals. Moreover, the inclusion of additional penalty factors in the weight computation procedure, assists in reducing fitting and prediction errors while simultaneously providing increased likelihood estimates. This modeling approach can be readily applied to other epidemics, both existing and emerging, where uncertainties in system dynamics and real-time observations hinder the accurate capture of the epidemic’s progression.

Model uncertainty in a parametric fire curve approach: A stochastic correction factor for the compartment fire load density

A commonly used approach to represent the thermal load in a compartment fire is the Eurocode Parametric Fire Curve (EPFC), which specifies gas temperatures (or rather adiabatic surface temperatures). Recognizing the significant deviations between real fires and the EPFC framework, the concept of model uncertainty is explored. This study does not aim to assess or improve the EPFC, but introduces a model uncertainty, allowing for reliability-based structural fire engineering (SFE). It presents a stochastic correction factor for the fire load density, based on the maximum temperature in steel sections. The focus is on the fire load density, but in general other parameters can be jointly taken into account as well. This correction factor considers protected and unprotected sections, incorporating variations in section factor and protection thickness. The findings reveal that the fire load density within the EPFC framework can be modified to better represent the severity of fire experiments. This approach ensures physical consistency of the obtained compartment gas temperatures, as opposed to alternative approaches for addressing the EPFC model uncertainty. While promising results are evident in this proof of concept, exploration for other types of structural elements and evaluation for structural systems is necessary before integration into design practices.

A Continuous Time Framework for Sequential Goal-Based Wealth Management

We develop a continuous time framework for sequential goals-based wealth management. A stochastic factor process drives asset price dynamics and the client’s goal amount and income. We prove the weak dynamic programming principle for the value function of our control problem, which we show to be the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. We develop an equivalent and computationally efficient representation of the Hamiltonian, which yields the optimal portfolio within a factor-dependent opportunity set defined by the maximum and minimum variance hypersurfaces. Our analysis shows that it is optimal to fund an expiring goal up to the level where the marginal benefit of additional fundedness is exceeded by the opportunity cost of diverting wealth from future goals. An all-or-nothing investor is more risk averse toward an approaching goal deadline if well funded, but more risk seeking if not on track with upcoming goals, compared with an investor with flexible goals. This paper was accepted by David Simchi-Levi, finance. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Discovery Grant RGPIN-2020-06290] and Fi-Tek.