Stochastic Risk Research Articles

Analytical model for CO2-water displacement with rate-dependent phase permeability for geological storage

Analytical modelling is an effective tool for predicting reservoir behaviour under high uncertainties, like CO2 storage in aquifers, where multiple simulation runs are necessary for stochastic modelling and risk assessment. This paper formulates the Buckley-Leverett problem with x-dependent fractional flow. We derive a new analytical model for displacement of brine by CO2 accounting for (i) rate-dependent phase permeability during radial flows and (ii) radial flows of Forchheimer’s high-rate gas injection; this analytical model is also valid for (iii) linear flows during flooding in micro heterogeneous or composite cores and (iv) CO2-water flow upscaling in reservoir where layering is perpendicular to flux direction. An exact solution of the flow equation is based on the observation that the flux of each phase conserves along the characteristic trajectories. We discuss S-shape fractional flow function, which is typical for reservoir rocks. The solution includes formulae for phase saturations and fluxes and trajectories of the displacement CO2-water front and of the forward and rear mixture zone boundaries. Fast analytical model can be used for multivariate sensitivity study and sweep efficiency prediction.

Radiation exposure of patients undergoing multiple-slice CT scans in Romania

Abstract Ionizing radiation is largely used in medicine due to its role in the diagnosis and treatment of patients. In the past 50 years computed tomography (CT) has become indispensable for medical practice because it offers sub-millimeter cross-sectional imaging of any region of the body. New CT scanners use thinner slices, providing more accurate results, but also an increased radiation exposure with possible long-term harmful effects for the patients. The parameter used as an indicator of radiation dose in CT is the dose-length product (DLP). The study included 4507 patients who were CT scanned using a 16, 32, 64 or 128-slice CT machine. DLP was measured for head, sinuses, thorax, abdomen, pelvis, abdomen+pelvis, and trunk scans - regions for which the health authorities have established national diagnostic reference levels (DRL - the expected radiation dose received by a patient in CT). One-way ANOVA was used to analyse data considering the use of contrast agents, the gender, age, and weight of patients. Average DLP values were higher (up to 80%) than national DRL for all regions in 64 and 128-slice scans. The highest DLP values were registered in contrast CT for all scanners (p < 0.01); the maximum average (a threefold increase compared to DRL) was measured in the 32-slice sinuses contrast CT. Average DLP correlated with patients’ gender and weight (p < 0.01), but the influence was lower compared to the use of contrast agents. In conclusion, CT scans acquired using thinner slices lead to more accurate results and high-quality images, but the study suggests an increased radiation exposure. CT has an uncontestable contribution to a precise and rapid diagnosis, but more attention must be given to the stochastic effects risks associated with the radiation dose received during a CT scan. Are all scans necessary? Do all patients really need to receive high doses? The role of the practitioner is decisive, and the justifiable process is “a must” in all radiodiagnosis practices. Key messages • CT doses must be kept “as low as reasonably achievable” while maintaining diagnostic image quality. • Justification, dose limitation, and optimisation are fundamental principles of radioprotection.

Source-oriented stochastic health risk assessment of toxic metals in soil via a hybrid model and Monte Carlo simulation

Toxic metal contamination in soils poses significant hazards to the environment and human health; thus, quantitative assessment of the sources and risks of metal contaminants are urgently needed. A hybrid model that integrates the positive matrix factorization (PMF) and random forest (RF) methods was proposed to quantify the sources of toxic metals in soils by combining diverse environmental variables (source proxies) in this study. In addition, a health risk assessment and Monte Carlo simulations were integrated to estimate the source-oriented stochastic health risk. The results suggested that, except for Ni, which exhibited moderate contamination, other toxic metals (As, Cd, Cr, Hg and Pb) presented slight contamination. Four sources (agricultural activities loaded heavily by As, atmospheric deposition loaded heavily by Hg and Pb, natural sources and mining activities loaded heavily by Cr and Ni, and industrial activities loaded heavily by Cd) were defined and explained 23.44 %, 26.65 %, 30.13 % and 19.78 % of the total variance in toxic metals, respectively. The principal route of exposure (i.e., ingestion), the population at highest risk (i.e., children), and the most hazard-inducing metals (i.e., As and Cr) were determined. Agricultural activities and the combination of natural sources and mining activities demonstrated certain degrees of noncarcinogenic risk to children, with exceedance ratios of 2.20 % and 2.56 %, respectively. Additionally, the combination of natural sources and mining activities demonstrated probabilities for significant carcinogenic risk to adults and children of 0.59 % and 3.76 %, respectively. To reduce the health risks of toxic metals in soils and to protect food and ecological safety, strict regulations should be established to control the discharge of waste from mining and agricultural activities.

Stochastic health risk assessment of aflatoxin M1 in cow's milk among Lebanese population

This study quantitatively assessed AFM1 exposure through consumption of cows' milk in Lebanese adolescents and adults. Lebanon-specific, non-aggregated data on (i) milk intake and body weight – from an existing survey for adults and from a new survey for adolescents, and (ii) AFM1 occurrence in milk, were fitted to distributions and incorporated into a probabilistic model. Risk of hepatocellular carcinoma (HCC) for milk consumers was estimated considering the incidence of hepatitis B virus in Lebanon and characterized using the margin of exposure (MOE). All subgroups’ mean risk estimates, expressed as additional HCC cases per 100 000 population per year, were significantly different (p < 0.05), and ranged from 2.2x10−4 for adult males to 4.9x10−4 for adolescent males. This variation is attributed to significant differences in body weight and milk intake. MOE identified adolescent males and females as at-risk populations (mean 9628 and 8108, respectively). For adults, levels of concern were only reached with extreme consumption and/or contamination events. Considering that exposure from other sources (e.g., dairy) is cumulative, control of AFM1 in milk in Lebanon should be a risk management priority to ensure protection of younger populations.

Comparison of directly and indirectly estimated entrance skin dose (ESD) for diagnostic radiation qualities (RQR, RQA and RQT) using water phantom and shadowfree diagnostic chamber (SFD)

BackgroundThe aim of this study was to find the entrance skin dose (ESD) for diagnostic radiation qualities RQRs, RQAs and RQTs given in IAEA technical report series No. 457 using direct and indirect methods of measurement. Measurements were done for 5 × 5, 10 × 10, 15 × 15, 20 × 20 and 25 × 25 cm2 field sizes and 70, 80, 90 and 100 cm source to surface distance (SSD) using shadow-free diagnostic (SFD) chamber and water phantom having dimension 30 × 30 × 30 cm3. ESD direct measurements were done by placing SFD chamber on the surface of water phantom, while in the case of indirect measurements, air kerma values were obtained.ResultsESD values for different selected radiation qualities RQR2, RQR5, RQR8, RQR10, RQA2, RQA5, RQA8, RQA10, RQT8, RQT9 and RQT10 were found to be in the range of 0.0045–5.11 mGy per examination.ConclusionsResults obtained were found to be comparable with ESD values published in the literature. The obtained results in this research would help in establishing the national diagnostic reference levels (DRLs) which would help in the optimization of diagnostic imaging procedures. It would also help the radiographers to optimize field sizes and SSDs in order to reduce dose to the patients thereby ensuring good radiological practices, and this would reduce the stochastic risk to the patients caused by the ionizing radiations.

Meta-analysis of soil and dust ingestion studies

The ingestion of soil and dust by children and adults is a potential source of exposure to environmental contaminants. To advance beyond the simple averaging of estimates used in the U.S. EPA's Exposure Factors Handbook (EFH), we describe a novel meta-analysis of all available studies that provided soil or dust ingestion estimates for children or adults conducted in the United States and Canada. Using meta-analytic techniques, we estimate the mean total soil plus dust ingestion rates and confidence intervals (CIs) for eleven age groups (0 - <1 month (m), 1 - <3 m, 3 - <6 m, 6 - <12 m, 1 - <2 years (y), 2 - <3 y, 3 - <6 y, 6 - <11 y, 11 - <16 y, 16 - <21 y, and 21+ y). These age groups were selected for consistency with the EFH update to Chapter 5 and the U.S. EPA's Age Grouping Guidance. For each age group, we calculated best estimates for the three main types of ingestion studies: tracer studies based on the aluminum tracer, biokinetic studies, and activity pattern (modeling) studies, as well as overall estimates for all three study types combined. Our meta-analysis combined study estimates using the alternative statistical approaches of the fixed effect method (inverse variance method, “I–V”) and two random effects methods, DerSimonian and Laird's method of moments (“DSL”) and the restricted maximum likelihood method (“MIXED”). For each approach, the mean total soil plus dust ingestion rate estimates for each study type generally aligned well with the EFH, ranging from 36 to 68 mg/day for infants, 56–72 mg/day for young children, and 12–32 mg/day for adolescents and adults. When all three study types were combined, the upper bounds of the 95% CI were generally the lowest for the I–V method and the highest for the MIXED method. The estimates produced here can be used for stochastic risk assessments and provide a better estimate of soil and dust ingestion rates across age groups.

Optimizing neurointerventional procedures: an algorithm for embolization coil detection and automated collimation to enable dose reduction.

Monitoring radiation dose and time parameters during radiological interventions is crucial, especially in neurointerventional procedures, such as aneurysm treatment with embolization coils. The algorithm presented detects the presence of these embolization coils in medical images. It establishes a bounding box as a reference for automated collimation, with the primary objective being to enhance the efficiency and safety of neurointerventional procedures by actively optimizing image quality while minimizing patient dose. Two distinct methodologies are evaluated in our study. The first involves deep learning, employing the Faster R-CNN model with a ResNet-50 FPN as a backbone and a RetinaNet model. The second method utilizes a classical blob detection approach, serving as a benchmark for comparison. We performed a fivefold cross-validation, and our top-performing model achieved mean mAP@75 of 0.84 across all folds on validation data and mean mAP@75 of 0.94 on independent test data. Since we use an upscaled bounding box, achieving 100% overlap between ground truth and prediction is not necessary. To highlight the real-world applications of our algorithm, we conducted a simulation featuring a coil constructed from an alloy wire, effectively showcasing the implementation of automatic collimation. This resulted in a notable reduction in the dose area product, signifying the reduction of stochastic risks for both patients and medical staff by minimizing scatter radiation. Additionally, our algorithm assists in avoiding extreme brightness or darkness in X-ray angiography images during narrow collimation, ultimately streamlining the collimation process for physicians. To our knowledge, this marks the initial attempt at an approach successfully detecting embolization coils, showcasing the extended applications of integrating detection results into the X-ray angiography system. The method we present has the potential for broader application, allowing its extension to detect other medical objects utilized in interventional procedures.

Closed‐Form Formulae for Variance and Volatility Swaps Under Stochastic Volatility With Stochastic Liquidity Risks

ABSTRACTWe construct a stochastic volatility model considering stochastic liquidity risks when valuing variance and volatility swaps with discrete sampling. We base our model on Heston stochastic volatility, which is adopted for the modeling of stock prices when the market is perfectly liquid. Stock dynamics are further revised by discounting their prices through the employment of mean reverting market liquidity. We convert the stock dynamics under the physical measure into the one under a risk‐neutral measure via measure transform, with which the analytical valuation of variance and volatility swaps is realized. By taking the limit of sampling frequency, we further consider how both swaps with continuous sampling can be priced. Numerical implementation is finally carried out, with which the capability of the constructed model in capturing the influence of the two common types of financial risks can be clear.

Stochastic coastal flood risk modelling for the east coast of Africa

Coastal flooding resulting from tropical cyclones can have large repercussions in many low-lying regions around the world. Accurate flood risk assessments are crucial for designing measures to reduce the societal impacts of coastal flooding. At continental to global scales, however, traditional flood risk assessments mostly use methods that do not capture the spatiotemporal dynamics of coastal flood risk patterns. In this study, we address these deficiencies by applying a novel modelling framework that dynamically simulates stochastic coastal flood risk for the east coast of Africa. Using 10,000 years of synthetic tropical cyclones and a cascade of hydrodynamic models to simulate storm tides and flooding, we calculate the damage of each individual tropical cyclone event and empirically derive the risk curve for each country. Results show that the largest aggregated annual losses in the region come from multiple events rather than from a single low-probability event. Results also reveal that events with the highest return periods in terms of storm surge residual levels and flood extents are not necessarily the most damaging events. Here, the 1 in 10,000-year damage event is associated with a 1 in 45-year event in terms of flood extent, showing that addressing exposure and vulnerability is essential in determining risk. Our modelling framework enables a high-resolution continental-scale risk analysis that takes the spatial dependencies of flood events into account.

Valuations of generalized variance swaps under the jump–diffusion model with stochastic liquidity risk

This paper focuses on the pricing problem of generalized variance swaps with jump risk in the underlying asset price under a stochastic liquidity model. We obtain a pricing formula of generalized variance swap in a jump–diffusion model with stochastic liquidity risk by the joint moment generating function (MGF) generated by solving the partial integral differential equation (PIDE). Using asymptotic analysis, we also demonstrate that as the sampling interval approaches zero, the pricing formula of discretely sampled generalized variance swap tends to be that of continuously sampled generalized variance swap. Finally, to verify the feasibility of the pricing formula of the generalized variance swap presented in this paper, we conduct some numerical experiments, including a comparison with the results of Monte Carlo (MC) simulation, the impact of various model parameters on the delivery prices of generalized variance swaps, and empirical research using actual market data.

A Divestment Model: Migration to Green Energy Investment Portfolio Concept

In a targeted terminal wealth generated by bond and risky assets, where the proportion of a risky asset is gradually being phased down, we propose a divestment model in a risky asset compensated by growth in a bond (insurance). The model includes the phase-down rate of the risky asset, c(t), the variable proportion, π(t), in a risky asset and the interest rate, r, of the bond. To guide the growth of the total wealth in this study, we compared it to the Øksendal and Sulem (Backward Stochastic Differential Equations and Risk Measures (2019)) total wealth for which c(t)=0, and π(t) is a constant. We employed the Fokker–Planck equation to find the variable moment, π(t), and the associated variance. We proved the existence and uniqueness of the first moment by Feller’s criteria. We have found a pair (c*(t),r*) for each π(t), which guarantees a growing total wealth. We have addressed the question whether this pair can reasonably be achieved to ensure an acceptable phase-down rate at a financially achievable interest rate, r*.

Pricing vulnerable spread options with liquidity risk under Lévy processes

In this paper, we consider vulnerable spread options with stochastic liquidity risk. Lévy processes are introduced to characterize jumps and we allow the liquidity discount factor to be related to a mean-reversion process. Through bivariate Fourier transforms, we successfully get the approximated pricing formula in the proposed model, and numerical experiments show that the approximated prices are very accurate. We finally focus on the impact of asymmetric jump risk and stochastic liquidity risk on vulnerable spread option prices.

Determining bid-ask prices for options with stochastic illiquidity and applications to index options

Market makers must quote two prices - bid and ask prices - for options. This article provides a GARCH model with stochastic illiquidity risks and gives analytical approximation solutions for the bid and ask prices for options. A joint calibration method is applied for calibrating the implied parameters. The empirical evidence shows an illiquidity smile for short-term calls and a negatively sloped illiquidity smirk for long-term calls. Similar results are also observed in put option prices. The proposed stochastic illiquidity model significantly outperforms the static illiquidity model in the in-sample and out-of-sample tests, particularly when the stochastic volatility is crucial.

Actuarial Valuation and Hedging of Life Insurance Liabilities in the Presence of Stochastic Mortality Risk under the Locally Risk-Minimizing Hedging Approach

The paper examines the valuation and hedging of life insurance obligations in the presence of mortality risk using the local risk-minimizing hedging approach. Roughly speaking, it is assumed that the lifetime of policyholders in an insurance portfolio is modeled by a point process whose stochastic intensity is controlled by a diffusion process. The stock price process is assumed to be a regime-switching Lévy process with non-zero regime-switching drift, where the parameters are assumed to depend on the economic states. Using the Föllmer–Schweizer decomposition, the main valuation and hedging results for a conditional payment process are determined. Some specific situations have been considered in which the local risk-minimizing strategies for a stream of liability payments or a unit-linked contract are presented.

Integrating meta-analysis with a quantitative microbial risk assessment model to investigate Campylobacter contamination of broiler carcasses

This study investigated the prevalence and associated risk factors of Campylobacter in South Korean broilers using a random-effects meta-analysis. Subsequently, to facilitate the design of preventive measures, the prevalence estimate from the meta-analysis was incorporated into a stochastic risk assessment model to quantify the Campylobacter contamination levels on broiler carcasses. The baseline model was developed based on the most common practices along the South Korean broiler processing line, with no interventions. Meta-analysis results revealed Campylobacter prevalence across the chicken supply chain in the following order: farms (60.6 % [57.3–63.4]), retail markets (43.90 % [24.81–64.99]), slaughterhouses (27.71 % [18.56–39.21]), and processing plants (14.50 % [3.96–41.09]). The model estimated a 52 % (36.1–70.8) Campylobacter prevalence at the end of chilling, with an average contamination level of 4.62 (2.50–6.74) log CFU/carcass. Sensitivity analysis indicated that Campylobacter fecal shedding (r = 0.95) and the amount of feces on bird exteriors (r = 0.17) at pre-harvest were the main factors for carcass contamination, while soft scalding (r = -0.22) and air chilling (r = -0.12) can serve as critical control points (CCPs) at harvest. Scenario analysis indicated that a combination of hard scalding, inside-outside bird washing, spray washing, and chlorinated water immersion chilling can offer a 30.9 % reduction in prevalence and a reduction of 2.23 log CFU/carcass in contamination levels compared to the baseline model. Apart from disinfection and sanitation interventions carried out during meat processing, the implementation of robust control measures is indispensable to mitigate Campylobacter prevalence and concentration at broiler farms, thereby enhancing meat safety and public health. Furthermore, given the high Campylobacter prevalence in the retail markets, future studies should explore the potential risk of cross-contamination at post-harvest stage.

Inventory management and delivery of perishable products with stochastic demands and risks consideration

In the agri-food supply chain, the perishable nature of the commodities opens a series of challenges at all decision levels: strategical, tactical and operational. This paper presents an age-based model for the inventory-routing problem of perishable commodities with stochastic demands. To deal with this source of uncertainty, the conditional value-at-risk (CVaR) has been adopted as a risk measure, and then the model has been applied to the agri-food supply chain under investigation. The model is the core of a dynamic approach for the optimal distribution and inventory planning over a short-medium horizon. To address a problem as realistic as possible, we assume that the demand for products of each age is unknown and we model this uncertainty by means of random variables with a probability distribution that can be estimated from historical data. Computational experiments on test cases based on a real-life agri-food company located in Italy show the effectiveness of the proposed approach for evaluating different risk attitudes.

Malcoda: Practical and Stochastic Security Risk Assessment for Enterprise Networks

Malcoda: Practical and Stochastic Security Risk Assessment for Enterprise Networks

Stochastic Precipitation Model Using Large Ensemble Data

A precipitation dataset is created to estimate a reproduction period of several thousand years for stochastic flood risk assessment in the non-life insurance sector. A stochastic precipitation model for natural hazard risk assessment developed in a previous study was applied to a large ensemble data. The model was used to obtain the precipitation ensembles for the recent and future climate by +2 K and +4 K increases in mean temperature, respectively. We successfully created 10,000 years of precipitation data, which makes it possible to obtain precipitation data over a 1,000-year return period.

Impact of Supply Risk Sharing on Supply Chains: Multiplicative vs. Additive Risks

Abstract We consider a supply chain in which a retailer orders from a manufacturer(s) who face(s) a stochastic supply risk (random yield) under single or dual-sourcing cases. In specific, we look into this problem in two different yield risks: multiplicative and additive. One might intuit that if the retailer shares a manufacturer’s random yield risk with the manufacturer, the manufacturer will be better off. Interestingly, we confirm that this intuition is only valid in the additive yield risk but not necessarily in the multiplicative yield risk. Moreover, under dual sourcing, both manufacturers fiercely compete on their prices (i.e., Bertrand-like competition) to become the sole source in the additive yield risk, but the manufacturers do not compete as much in the multiplicative yield risk. Lastly, this paper shows that the supply chain inefficiency may decrease (increase) as risk-sharing increases in the additive risk model under dual sourcing (single sourcing) while it does not changeinthemultiplicativeriskmodel. Key words: supply risk, random yield, dual sourcing, game theory JEL Classification: L11, M11, M21

Enhancing Strategic Planning of Projects: Selecting the Right Product Development Methodology

The selection of an appropriate development methodology is a critical strategic decision when managing a New Product Development (NPD) project. However, accurately estimating project duration based on the chosen methodology remains a challenge. This paper addresses the limitations of existing models and proposes a novel NPD project model that allows for testing and evaluation of different product development strategies. The model considers Waterfall, Spiral, Agile, and Hybrid methodologies and provides system engineers and project managers with decision-making tools to determine the optimal strategy and understand associated tradeoffs. The model is validated using real projects from various organizations and methodologies. It incorporates stochastic variables, risk management, and dynamic resource allocation, while addressing both Waterfall and Agile methodologies. The study contributes to the body of knowledge by offering practical tools for system engineers and project managers for choosing development methodology, improving project duration estimation, and identifying critical processes and risks in NPD projects. The research results also provide a basis for further studies and can benefit researchers interested in systems engineering methodologies. The proposed model fills a gap in the literature by providing a validated NPD model to evaluate the impact of different product development methodologies on project duration.