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## The Martingale Options Price Valuation for European Puts Using Stochastic Differential Equation Models

In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

## Monte Carlo Estimation of Heteroscedasticity and Periodicity Effects in a Panel Data Regression Model

This research attempts to investigate the effects of heteroscedasticity and periodicity in a Panel Data Regression Model (PDRM) by extending previous works on balanced panel data estimation within the context of fitting PDRM for Banks audit fee. The estimation of such model was achieved through the derivation of Joint Lagrange Multiplier (LM) test for homoscedasticity and zero-serial correlation, a conditional LM test for zero serial correlation given heteroscedasticity of varying degrees as well as conditional LM test for homoscedasticity given first order positive serial correlation via a two-way error component model. Monte Carlo simulations were carried out for 81 different variations, of which its design assumed a uniform distribution under a linear heteroscedasticity function. Each of the variation was iterated 1000 times and the assessment of the three estimators considered are based on Variance, Absolute bias (ABIAS), Mean square error (MSE) and the Root Mean Square (RMSE) of parameters estimates. Eighteen different models at different specified conditions were fitted, and the best-fitted model is that of within estimator when heteroscedasticity is severe at either zero or positive serial correlation value. LM test results showed that the tests have good size and power as all the three tests are significant at 5% for the specified linear form of heteroscedasticity function which established the facts that Banks operations are severely heteroscedastic in nature with little or no periodicity effects.

## Modeling Football Penalty Shootouts: How Improving Individual Performance Affects Team Performance and the Fairness of the ABAB Sequence

Penalty shootouts often decide the outcome of important soccer matches. Although usually referred to as ”lotteries”, there is evidence that some national teams and clubs consistently perform better than others. The outcomes are therefore not explained just by mere luck, and therefore there are ways to improve the average performance of players, naturally at the expense of some sort of effort. In this article we study the payoff of player performance improvements in terms of the performance of the team as a whole. To do so we develop an analytical model with static individual performances, as well as Monte Carlo models that take into account the known influence of partial score and round number on individual performances. We find that within a range of usual values, the team performance improves above 70% faster than individual performances do. Using these models, we also estimate that the new ABBA penalty shootout ordering under test reduces almost all the known bias in favor of the first-shooting team under the current ABAB system.

## Jeffrey's Prior for Unknown Sinusoidal Noise Model via Cramer-Rao Lower Bound

This paper employs the Jeffrey's prior technique in the process of estimating the periodograms and frequency of sinusoidal model for unknown noisy time variants or oscillating events (data) in a Bayesian setting. The non-informative Jeffrey's prior was adopted for the posterior trigonometric function of the sinusoidal model such that Cramer-Rao Lower Bound (CRLB) inference was used in carving-out the minimum variance needed to curb the invariance structure effect for unknown noisy time observational and repeated circular patterns. An average monthly oscillating temperature series measured in degree Celsius (0C) from 1901 to 2014 was subjected to the posterior solution of the unknown noisy events of the sinusoidal model via Markov Chain Monte Carlo (MCMC). It was not only deduced that two minutes period is required before completing a cycle of changing temperature from one particular degree Celsius to another but also that the sinusoidal model via the CRLB-Jeffrey's prior for unknown noisy events produced a miniature posterior Maximum A Posteriori (MAP) compare to a known noisy events.

## The Influence of Beta Shape Parameters in Project Planning

Networks can be utilized to represent project planning problems, using nodes for activities and arcs to indicate precedence relationship between them. For fixed activity duration, a simple algorithm calculates the amount of time required to complete a project, followed by the activities that comprise the critical path. Program Evaluation and Review Technique (PERT) generalizes the above model by incorporating uncertainty, allowing activity durations to be random variables, producing nevertheless a relatively crude solution in planning problems. In this paper, based on the findings of the relevant literature, which strongly suggests that a Beta distribution can be employed to model earthmoving activities, we utilize Monte Carlo simulation, to estimate the project completion time distribution and measure the influence of skewness, an element inherent in activities of modern technical projects. We also extract the activity criticality index, with an ultimate goal to produce more accurate planning estimations.

## Economic Evaluation Offshore Wind Project under Uncertainly and Risk Circumstances

Offshore wind energy as a strategic renewable energy, has been growing rapidly due to availability, abundance and clean nature of it. On the other hand, budget of this project is incredibly higher in comparison with other renewable energies and it takes more duration. Accordingly, precise estimation of time and cost is needed in order to promote awareness in the developers and society and to convince them to develop this kind of energy despite its difficulties. Occurrence risks during on project would cause its duration and cost constantly changed. Therefore, to develop offshore wind power, it is critical to consider all potential risks which impacted project and to simulate their impact. Hence, knowing about these risks could be useful for the selection of most influencing strategies such as avoidance, transition, and act in order to decrease their probability and impact. This paper presents an evaluation of the feasibility of 500 MV offshore wind project in the Persian Gulf and compares its situation with uncertainty resources and risk. The purpose of this study is to evaluate time and cost of offshore wind project under risk circumstances and uncertain resources by using Monte Carlo simulation. We analyzed each risk and activity along with their distribution function and their effect on the project.

## Probabilistic Life Cycle Assessment of the Nano Membrane Toilet

Developing countries are nowadays confronted with great challenges related to domestic sanitation services in view of the imminent water scarcity. Contemporary sanitation technologies established in these countries are likely to pose health risks unless waste management standards are followed properly. This paper provides a solution to sustainable sanitation with the development of an innovative toilet system, called Nano Membrane Toilet (NMT), which has been developed by Cranfield University and sponsored by the Bill & Melinda Gates Foundation. The particular technology converts human faeces into energy through gasification and provides treated wastewater from urine through membrane filtration. In order to evaluate the environmental profile of the NMT system, a deterministic life cycle assessment (LCA) has been conducted in SimaPro software employing the Ecoinvent v3.3 database. The particular study has determined the most contributory factors to the environmental footprint of the NMT system. However, as sensitivity analysis has identified certain critical operating parameters for the robustness of the LCA results, adopting a stochastic approach to the Life Cycle Inventory (LCI) will comprehensively capture the input data uncertainty and enhance the credibility of the LCA outcome. For that purpose, Monte Carlo simulations, in combination with an artificial neural network (ANN) model, have been conducted for the input parameters of raw material, produced electricity, NOX emissions, amount of ash and transportation of fertilizer. The given analysis has provided the distribution and the confidence intervals of the selected impact categories and, in turn, more credible conclusions are drawn on the respective LCIA (Life Cycle Impact Assessment) profile of NMT system. Last but not least, the specific study will also yield essential insights into the methodological framework that can be adopted in the environmental impact assessment of other complex engineering systems subject to a high level of input data uncertainty.

## Fragility Analysis of Weir Structure Subjected to Flooding Water Damage

In this study, seepage analysis was performed by the level difference between upstream and downstream of weir structure for safety evaluation of weir structure against flooding. Monte Carlo Simulation method was employed by considering the probability distribution of the adjacent ground parameter, i.e., permeability coefficient of weir structure. Moreover, by using a commercially available finite element program (ABAQUS), modeling of the weir structure is carried out. Based on this model, the characteristic of water seepage during flooding was determined at each water level with consideration of the uncertainty of their corresponding permeability coefficient. Subsequently, fragility function could be constructed based on this response from numerical analysis; this fragility function results could be used to determine the weakness of weir structure subjected to flooding disaster. They can also be used as a reference data that can comprehensively predict the probability of failur,e and the degree of damage of a weir structure.

## A Dose Distribution Approach Using Monte Carlo Simulation in Dosimetric Accuracy Calculation for Treating the Lung Tumor

This paper presents a Monte Carlo (MC) method-based dose distributions on lung tumor for 6 MV photon beam to improve the dosimetric accuracy for cancer treatment. The polystyrene which is tissue equivalent material to the lung tumor density is used in this research. In the empirical calculations, TRS-398 formalism of IAEA has been used, and the setup was made according to the ICRU recommendations. The research outcomes were compared with the state-of-the-art experimental results. From the experimental results, it is observed that the proposed based approach provides more accurate results and improves the accuracy than the existing approaches. The average %variation between measured and TPS simulated values was obtained 1.337±0.531, which shows a substantial improvement comparing with the state-of-the-art technology.

## Optimization of Air Pollution Control Model for Mining

The sustainable measures on air quality management are recognized as one of the most serious environmental concerns in the mining region. The mining operations emit various types of pollutants which have significant impacts on the environment. This study presents a stochastic control strategy by developing the air pollution control model to achieve a cost-effective solution. The optimization method is formulated to predict the cost of treatment using linear programming with an objective function and multi-constraints. The constraints mainly focus on two factors which are: production of metal should not exceed the available resources, and air quality should meet the standard criteria of the pollutant. The applicability of this model is explored through a case study of an open pit metal mine, Utah, USA. This method simultaneously uses meteorological data as a dispersion transfer function to support the practical local conditions. The probabilistic analysis and the uncertainties in the meteorological conditions are accomplished by Monte Carlo simulation. Reasonable results have been obtained to select the optimized treatment technology for PM2.5, PM10, NOx, and SO2. Additional comparison analysis shows that baghouse is the least cost option as compared to electrostatic precipitator and wet scrubbers for particulate matter, whereas non-selective catalytical reduction and dry-flue gas desulfurization are suitable for NOx and SO2 reduction respectively. Thus, this model can aid planners to reduce these pollutants at a marginal cost by suggesting control pollution devices, while accounting for dynamic meteorological conditions and mining activities.

## Evaluation of Wind Fragility for Set Anchor Used in Sign Structure in Korea

Recently, damage to domestic facilities by strong winds and typhoons are growing. Therefore, this study focused on sign structure among various vulnerable facilities. The evaluation of the wind fragility was carried out considering the destruction of the anchor, which is one of the various failure modes of the sign structure. The performance evaluation of the anchor was carried out to derive the wind fragility. Two parameters were set and four anchor types were selected to perform the pull-out and shear tests. The resistance capacity was estimated based on the experimental results. Wind loads were estimated using Monte Carlo simulation method. Based on these results, we derived the wind fragility according to anchor type and wind exposure category. Finally, the evaluation of the wind fragility was performed according to the experimental parameters such as anchor length and anchor diameter. This study shows that the depth of anchor was more significant for the safety of structure compare to diameter of anchor.

## Dynamic Correlations and Portfolio Optimization between Islamic and Conventional Equity Indexes: A Vine Copula-Based Approach

This study examines conditional Value at Risk by applying the GJR-EVT-Copula model, and finds the optimal portfolio for eight Dow Jones Islamic-conventional pairs. Our methodology consists of modeling the data by a bivariate GJR-GARCH model in which we extract the filtered residuals and then apply the Peak over threshold model (POT) to fit the residual tails in order to model marginal distributions. After that, we use pair-copula to find the optimal portfolio risk dependence structure. Finally, with Monte Carlo simulations, we estimate the Value at Risk (VaR) and the conditional Value at Risk (CVaR). The empirical results show the VaR and CVaR values for an equally weighted portfolio of Dow Jones Islamic-conventional pairs. In sum, we found that the optimal investment focuses on Islamic-conventional US Market index pairs because of high investment proportion; however, all other index pairs have low investment proportion. These results deliver some real repercussions for portfolio managers and policymakers concerning to optimal asset allocations, portfolio risk management and the diversification advantages of these markets.

## Wind Fragility for Soundproof Wall with the Variation of Section Shape of Frame

Recently, damages due to typhoons and strong wind are on the rise. Considering this issue, we evaluated the performance of soundproofing walls based on the strong wind fragility by means of numerical analysis. Among the components of the soundproof wall, aluminum frame was the most vulnerable member, thus we have considered different section of aluminum frame in the determination of wind fragility. Wind load was randomly generated using Monte Carlo Simulation method. Moreover, limit state was based on the test standard of road construction soundproofing wall. In this study, the strong wind fragility was determined by considering the influence factors of wind exposure category, soundproof wall’s installation position, and shape of aluminum frame section. Results of this study could be used to determine the section shape of the frame that has high resistance to the wind during construction of the soundproofing wall.

## Evaluation of the Mechanical Behavior of a Retaining Wall Structure on a Weathered Soil through Probabilistic Methods

Retaining slope structures are increasingly considered in geotechnical engineering projects due to extensive urban cities growth. These kinds of engineering constructions may present instabilities over the time and may require reinforcement or even rebuilding of the structure. In this context, statistical analysis is an important tool for decision making regarding retaining structures. This study approaches the failure probability of the construction of a retaining wall over the debris of an old and collapsed one. The new solution’s extension length will be of approximately 350 m and will be located over the margins of the Lake Paranoá, Brasilia, in the capital of Brazil. The building process must also account for the utilization of the ruins as a caisson. A series of in situ and laboratory experiments defined local soil strength parameters. A Standard Penetration Test (SPT) defined the in situ soil stratigraphy. Also, the parameters obtained were verified using soil data from a collection of masters and doctoral works from the University of Brasília, which is similar to the local soil. Initial studies show that the concrete wall is the proper solution for this case, taking into account the technical, economic and deterministic analysis. On the other hand, in order to better analyze the statistical significance of the factor-of-safety factors obtained, a Monte Carlo analysis was performed for the concrete wall and two more initial solutions. A comparison between the statistical and risk results generated for the different solutions indicated that a Gabion solution would better fit the financial and technical feasibility of the project.

## Wind Fragility for Honeycomb Roof Cladding Panels Using Screw Pull-Out Capacity

The failure of roof cladding mostly occurs due to the failing of the connection between claddings and purlins, which is the pull-out of the screw connecting the two parts when the pull-out load, i.e. typhoon, is higher than the resistance of the connection screw. As typhoon disasters in Korea are constantly on the rise, probability risk assessment (PRA) has become a vital tool to evaluate the performance of civil structures. In this study, we attempted to determine the fragility of roof cladding with the screw connection. Experimental study was performed to evaluate the pull-out resistance of screw joints between honeycomb panels and back frames. Subsequently, by means of Monte Carlo Simulation method, probability of failure for these types of roof cladding was determined. The results that the failure of roof cladding was depends on their location on the roof, for example, the edge most panel has the highest probability of failure.

## Reliability Based Performance Evaluation of Stone Column Improved Soft Ground

The present study considers the effect of variation of different geotechnical random variables in the design of stone column-foundation systems for assessing the bearing capacity and consolidation settlement of highly compressible soil. The soil and stone column properties, spacing, diameter and arrangement of stone columns are considered as the random variables. Probability of failure (Pf) is computed for a target degree of consolidation and a target safe load by Monte Carlo Simulation (MCS). The study shows that the variation in coefficient of radial consolidation (cr) and cohesion of soil (cs) are two most important factors influencing Pf. If the coefficient of variation (COV) of cr exceeds 20%, Pf exceeds 0.001, which is unsafe following the guidelines of US Army Corps of Engineers. The bearing capacity also exceeds its safe value for COV of cs > 30%. It is also observed that as the spacing between the stone column increases, the probability of reaching a target degree of consolidation decreases. Accordingly, design guidelines, considering both consolidation and bearing capacity of improved ground, are proposed for different spacing and diameter of stone columns and geotechnical random variables.

## Performance Analysis of the Time-Based and Periodogram-Based Energy Detector for Spectrum Sensing

Classically, an energy detector is implemented in time domain (TD). However, frequency domain (FD) based energy detector has demonstrated an improved performance. This paper presents a comparison between the two approaches as to analyze their pros and cons. A detailed performance analysis of the classical TD energy-detector and the periodogram based detector is performed. Exact and approximate mathematical expressions for probability of false alarm (Pf) and probability of detection (Pd) are derived for both approaches. The derived expressions naturally lead to an analytical as well as intuitive reasoning for the improved performance of (Pf) and (Pd) in different scenarios. Our analysis suggests the dependence improvement on buffer sizes. Pf is improved in FD, whereas Pd is enhanced in TD based energy detectors. Finally, Monte Carlo simulations results demonstrate the analysis reached by the derived expressions.

## Seismic Fragility for Sliding Failure of Weir Structure Considering the Process of Concrete Aging

This study investigated the change of weir structure performances when durability of concrete, which is the main material of weir structure, decreased due to their aging by mean of seismic fragility analysis. In the analysis, it was assumed that the elastic modulus of concrete was reduced by 10% in order to account for their aged deterioration. Additionally, the analysis of seismic fragility was based on Monte Carlo Simulation method combined with a 2D nonlinear finite element in ABAQUS platform with the consideration of deterioration of concrete. Finally, the comparison of seismic fragility of model pre- and post-deterioration was made to study the performance of weir. Results show that the probability of failure in moderate damage for deteriorated model was found to be larger than pre-deterioration model when peak ground acceleration (PGA) passed 0.4 g.

## Probability-Based Damage Detection of Structures Using Kriging Surrogates and Enhanced Ideal Gas Molecular Movement Algorithm

Surrogate model has received increasing attention for use in detecting damage of structures based on vibration modal parameters. However, uncertainties existing in the measured vibration data may lead to false or unreliable output result from such model. In this study, an efficient approach based on Monte Carlo simulation is proposed to take into account the effect of uncertainties in developing a surrogate model. The probability of damage existence (PDE) is calculated based on the probability density function of the existence of undamaged and damaged states. The kriging technique allows one to genuinely quantify the surrogate error, therefore it is chosen as metamodeling technique. Enhanced version of ideal gas molecular movement (EIGMM) algorithm is used as main algorithm for model updating. The developed approach is applied to detect simulated damage in numerical models of 72-bar space truss and 120-bar dome truss. The simulation results show the proposed method can perform well in probability-based damage detection of structures with less computational effort compared to direct finite element model.

## Reduction of Plutonium Production in Heavy Water Research Reactor: A Feasibility Study through Neutronic Analysis Using MCNPX2.6 and CINDER90 Codes

One of the main characteristics of Heavy Water Moderated Reactors is their high production of plutonium. This article demonstrates the possibility of reduction of plutonium and other actinides in Heavy Water Research Reactor. Among the many ways for reducing plutonium production in a heavy water reactor, in this research, changing the fuel from natural Uranium fuel to Thorium-Uranium mixed fuel was focused. The main fissile nucleus in Thorium-Uranium fuels is U-233 which would be produced after neutron absorption by Th-232, so the Thorium-Uranium fuels have some known advantages compared to the Uranium fuels. Due to this fact, four Thorium-Uranium fuels with different compositions ratios were chosen in our simulations; a) 10% UO2-90% THO2 (enriched= 20%); b) 15% UO2-85% THO2 (enriched= 10%); c) 30% UO2-70% THO2 (enriched= 5%); d) 35% UO2-65% THO2 (enriched= 3.7%). The natural Uranium Oxide (UO2) is considered as the reference fuel, in other words all of the calculated data are compared with the related data from Uranium fuel. Neutronic parameters were calculated and used as the comparison parameters. All calculations were performed by Monte Carol (MCNPX2.6) steady state reaction rate calculation linked to a deterministic depletion calculation (CINDER90). The obtained computational data showed that Thorium-Uranium fuels with four different fissile compositions ratios can satisfy the safety and operating requirements for Heavy Water Research Reactor. Furthermore, Thorium-Uranium fuels have a very good proliferation resistance and consume less fissile material than uranium fuels at the same reactor operation time. Using mixed Thorium-Uranium fuels reduced the long-lived α emitter, high radiotoxic wastes and the radio toxicity level of spent fuel.