Search results for: Volatility.

Authors: Changhong Guo, Shaomei Fang, Yong He

Abstract:

In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes.

Keywords: European option pricing, fractional Black-Scholes equations, fractional G-Brownian motion, Taylor’s series of fractional order, uncertain volatility.

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Authors: Katleho D. Makatjane, Kalebe M. Kalebe

Abstract:

The present paper used time-varying parameters which are based on the score function of a probability density at time t to model volatility of saving rate. We used a scaled likelihood function to update the parameters of the model overtime. Our results revealed high diligence of time-varying since the location parameter is greater than zero. Furthermore, we discovered a leptokurtic condition on saving rate’s distribution. Kapetanios, Shin-Shell Nonlinear Augmented Dickey-Fuller (KSS-NADF) test showed that the saving rate has a nonlinear unit root; therefore, it can be modeled by a generalised autoregressive score (GAS) model. Additionally, value at risk (VaR) and conditional tail expectation (CTE) indicate that 99% of the time people in Lesotho are saving more than spending. This puts the economy in high risk of not expanding. Therefore, the monetary policy committee (MPC) of Lesotho should revise their monetary policies towards this high saving rates risk.

Keywords: Generalized autoregressive score, time-varying, saving rate, Lesotho.

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Authors: Robert Cep, Lenka Ocenasova, Jana Novakova, Karel Kouril, Jan Valicek, Branimir Barisic

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This paper deals with the problem of thermal and mechanical shocks, which rising during operation, mostly at interrupted cut. Here will be solved their impact on the cutting edge tool life, the impact of coating technology on resistance to shocks and experimental determination of tool life in heating flame. Resistance of removable cutting edges against thermal and mechanical shock is an important indicator of quality as well as its abrasion resistance. Breach of the edge or its crumble may occur due to cyclic loading. We can observe it not only during the interrupted cutting (milling, turning areas abandoned hole or slot), but also in continuous cutting. This is due to the volatility of cutting force on cutting. Frequency of the volatility in this case depends on the type of rising chips (chip size element). For difficult-to-machine materials such as austenitic steel particularly happened at higher cutting speeds for the localization of plastic deformation in the shear plane and for the inception of separate elements substantially continuous chips. This leads to variations of cutting forces substantially greater than for other types of steel.

Keywords: Cutting Tool Life, Heating, Mechanical Shocks, Thermal Shocks

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Authors: Andrea Paltrinieri, Alberto Dreassi, Stefano Miani, Alex Sclip

Abstract:

The financial crises caused a collapse in prices of most asset classes, raising the attention on alternative investments such as sukuk, a smaller, fast growing but often misunderstood market. We study diversification benefits of sukuk, their correlation with other asset classes and the effects of their inclusion in investment portfolios of institutional and retail investors, through a comprehensive comparison of their risk/return profiles during and after the financial crisis. We find a beneficial performance adjusted for the specific volatility together with a lower correlation especially during the financial crisis. The distribution of sukuk returns is positively skewed and leptokurtic, with a risk/return profile similarly to high yield bonds. Overall, our results suggest that sukuk present diversification opportunities, a significant volatility-adjusted performance and lower correlations especially during the financial crisis. Our findings are relevant for a number of institutional investors. Long term investors, such as life insurers would benefit from sukuk’s protective features during financial crisis yet keeping return and growth opportunities, whereas banks would gain due to their role of placers, advisors, market makers or underwriters.

Keywords: Asset allocation, asset performance, sukuk, zero beta asset.

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Authors: Attapong T., Hong-Ming Ku, Nakarin M., Narin L., Alisa L, Jirut W.

Abstract:

The quantum mechanics simulation was applied for calculating the interaction force between 2 molecules based on atomic level. For the simple extractive distillation system, it is ternary components consisting of 2 closed boiling point components (A,lower boiling point and B, higher boiling point) and solvent (S). The quantum mechanics simulation was used to calculate the intermolecular force (interaction force) between the closed boiling point components and solvents consisting of intermolecular between A-S and B-S. The requirement of the promising solvent for extractive distillation is that solvent (S) has to form stronger intermolecular force with only one component than the other component (A or B). In this study, the systems of aromatic-aromatic, aromatic-cycloparaffin, and paraffindiolefin systems were selected as the demonstration for solvent selection. This study defined new term using for screening the solvents called relative interaction force which is calculated from the quantum mechanics simulation. The results showed that relative interaction force gave the good agreement with the literature data (relative volatilities from the experiment). The reasons are discussed. Finally, this study suggests that quantum mechanics results can improve the relative volatility estimation for screening the solvents leading to reduce time and money consuming

Keywords: Extractive distillation, Interaction force, Quamtum mechanic, Relative volatility, Solvent extraction.

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Authors: Sara D. Garduño-Diaz, Philippe Y. Garduño-Diaz

Abstract:

To date, one of the few comprehensive indicators for the measurement of food security is the Global Food Security Index (GFSI). This index is a dynamic quantitative and qualitative benchmarking model, constructed from 28 unique indicators, that measures drivers of food security across both developing and developed countries. Whereas the GFSI has been calculated across a set of 109 countries, in this paper we aim to present and compare, for the Middle East and North Africa (MENA), 1) the Food Security Index scores achieved and 2) the data available on affordability, availability, and quality of food. The data for this work was taken from the latest available report published by the creators of the GFSI, which in turn used information from national and international statistical sources. MENA countries rank from place 17/109 (Israel, although with resent political turmoil this is likely to have changed) to place 91/109 (Yemen) with household expenditure spent in food ranging from 15.5% (Israel) to 60% (Egypt). Lower spending on food as a share of household consumption in most countries and better food safety net programs in the MENA have contributed to a notable increase in food affordability. The region has also, however, experienced a decline in food availability, owing to more limited food supplies and higher volatility of agricultural production. In terms of food quality and safety the MENA has the top ranking country (Israel). The most frequent challenges faced by the countries of the MENA include public expenditure on agricultural research and development as well as volatility of agricultural production. Food security is a complex phenomenon that interacts with many other indicators of a country’s wellbeing; in the MENA it is slowly but markedly improving.

Keywords: Diet, food insecurity, global food security index, nutrition, sustainability.

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Authors: Julian Becker, Wiebke Hartmann, Sebastian Bertsch, Johannes Nywlt, Matthias Schmidt

Abstract:

In order to ensure a high service level industrial enterprises have to maintain safety-stock that directly influences the economic efficiency at the same time. This paper analyses established mathematical methods to calculate safety-stock. Therefore, the performance measured in stock and service level is appraised and the limits of several methods are depicted. Afterwards, a new dynamic approach is presented to gain an extensive method to calculate safety-stock that also takes the knowledge of future volatility into account.

Keywords: Inventory dimensioning, material requirement planning, safety-stock calculation.

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Authors: Fatimah Almah Saaid, Darfiana Nur, Robert King

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This paper presents a procedure for estimating VAR using Sequential Discounting VAR (SDVAR) algorithm for online model learning to detect fraudulent acts using the telecommunications call detailed records (CDR). The volatility of the VAR is observed allowing for non-linearity, outliers and change points based on the works of [1]. This paper extends their procedure from univariate to multivariate time series. A simulation and a case study for detecting telecommunications fraud using CDR illustrate the use of the algorithm in the bivariate setting.

Keywords: Telecommunications Fraud, SDVAR Algorithm, Multivariate time series, Vector Autoregressive, Change points.

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Authors: Frantisek Bozek, Lenka Jesonkova, Jiri Dvorak

Abstract:

Trihalogenmethanes are the most significant byproducts of the reaction of disinfection agent with organic precursors naturally present in ground and surface waters.Their incidence negatively affects the quality of drinking water in relation to their nephrotoxic, hepatotoxic and genotoxic effects on human health. Taking into consideration the considerable volatility of monitored contaminants it could be assumed that their incidence in drinking water would depend on the distance of sampling from the area of disinfection. Based on the concentration of trihalogenmethanes determined with the help of gas chromatography with mass detector and the analysis of variance (ANOVA) such dependence has been proved as statistically significant. The acquired outcomes will be used for assessing the non-carcinogenic and genotoxic risks to consumers.

Keywords: disinfection byproducts, drinking water, trihalogenmethanes

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Authors: Larisa N. Pop, Irina M. Ban

Abstract:

This paper aims to present the main instruments used in the economic literature for measuring the price risk, pointing out on the advantages brought by the conditional variance in this respect. The theoretical approach will be exemplified by elaborating an EGARCH model for the price returns of wheat, both on Romanian and on international market. To our knowledge, no previous empirical research, either on price risk measurement for the Romanian markets or studies that use the ARIMA-EGARCH methodology, have been conducted. After estimating the corresponding models, the paper will compare the estimated conditional variance on the two markets.

Keywords: conditional variance, GARCH models, price risk, volatility

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Authors: Dhaksha Vivekanandan

Abstract:

DeFi is a network that avoids reliance on financial intermediaries through its peer-to-peer financial network. DeFi operates outside of government control; hence, it is important for us to understand its impacts. This study employs a literature review to understand DeFi and its emergence, as well as its implications on transparency, social impact, and regulation. Further, three case studies are analysed within the context of these categories. DeFi’s provision of increased transparency poses environmental and storage costs and can lead to user privacy being endangered. DeFi allows for the provision of entrepreneurial incentives and protection against monetary censorship and capital control. Despite DeFi's transparency issues and volatility costs, it has huge potential to reduce poverty; however, regulation surrounding DeFi still requires further tightening by governments.

Keywords: DeFi, transparency, regulation, social impact.

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Authors: Nikolaos Sariannidis, Grigoris Giannarakis, Nikolaos Litinas, Nikos Kartalis

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This study investigates the relationship between 10 year bond value, Yen/U.S dollar exchange rate, non-farm payrolls (all employs) and crude oil to U.S. Dow Jones Sustainability Index. A GARCH model is used to test these relationships for the period January 1st 1999 to January 31st 2008 using monthly data. Results show that an increase of the 10 year bond and non farm payrolls (all employs) lead to an increase of the D.J.S.I returns. On the contrary the volatility of the Yen/U.S dollar exchange rates as well as the increase of crude oil returns has negative effects on the U.S D.J.S.I returns. This study aims at assisting investors to understand the influences certain macroeconomic indicators have on the companies- stock returns as reported by the D.J.S.I.

Keywords: Bond value, Corporate Social Responsibility, Crudeoil, D.J.S.I United States, Exchange rate, GARCH, Non-farmpayrolls.

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Authors: Shashwat Gangwal

Abstract:

This paper analyses the effect of adding Bitcoin, to the portfolio (stocks, bonds, Baltic index, MXEF, gold, real estate and crude oil) of an international investor by using daily data available from 2^nd of July, 2010 to 2^{nd of} August, 2016. We conclude that adding Bitcoin to portfolio, over the course of the considered period, always yielded a higher Sharpe ratio. This means that Bitcoin’s returns offset its high volatility. This paper, recognizing the fact that Bitcoin is a relatively new asset class, gives the readers a basic idea about the working of the virtual currency, the increasing number developments in the financial industry revolving around it, its unique features and the detailed look into its continuously growing acceptance across different fronts (Banks, Merchants and Countries) globally. We also construct optimal portfolios to reflect the highly lucrative and largely unexplored opportunities associated with investment in Bitcoin.

Keywords: Portfolio management, Bitcoin, optimization, Sharpe ratio.

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Authors: Chih-Hsiang Chang

Abstract:

This study aims to explore the relationship between the disposition effect and herding behavior of investors trading Taiwanese information technology stocks. This study differs from previous literature in two aspects. First, in contrast with the earlier studies that focused on investigating investors’ herding behavior, this study explores the possibility that the disposition effect drives investors’ herding behavior. Additionally, it takes an in-depth look at the interdependence between the disposition effect and herding behavior of investors, including lead-lag relationship and volatility transmission effect. Empirical results show that investors trading Taiwan’s information technology stocks exhibit pronounced herding behavior and that the disposition effect has a great impact on their herding behavior.

Keywords: Herding behavior, Disposition effect, Behavioral finance.

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Authors: Ruma Bhattacharyya

Abstract:

The basic objective of this paper is to measure and compare the profitability of investments made by the small and marginal farmers of the state of West Bengal in floriculture shifting from the traditional cultivation of paddy. A comparison of IRR is made to establish the fact that cultivation of flowers yield higher returns farmers whose land size is so small that viability of paddy cultivation is raising a question mark. A detailed study of the price behavior of the flower crop has been carried out in which the factors leading to the volatility of the price and the dispersion of the range have also been discussed. Finally the incremental incomes of the farmers have been calculated with the help of imputed income from paddy cultivation and the reported income from the selected flowers. The study shows that the farmers stand gainers if they opt for flower cultivation.

Keywords: Bazar Samity, Floriculture, Marginal Farmers.

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Authors: M. G. Mattos, J. E. Pécora Jr, T. A. Briso

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Today's challenging business environment, with unpredictable demand and volatility, requires a supply chain strategy that handles uncertainty and risks in the right way. Even though inventory models have been previously explored, this paper seeks to apply these concepts on a practical situation. This study involves the inventory replenishment problem, applying techniques that are mainly based on mathematical assumptions and modeling. The primary goal is to improve the retailer’s supply chain processes taking store differences when setting the various target stock levels. Through inventory review policy, picking piece implementation and minimum exposure definition, we were able not only to promote the inventory reduction as well as improve sales results. The inventory management theory from literature review was then tested on a single case study regarding a particular department in one of the largest Latam retail chains.

Keywords: Inventory, distribution, retail, risk, safety stock, sales, uncertainty.

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Authors: Sebastian Bertsch

Abstract:

In the past decades, the environment of production companies showed a permanent increase in dynamic and volatility in the form of demand fluctuations, new technologies or global crises. As a reaction to these new requirements, changeability of production systems came into attention. A changeable production system can adapt to these changes quickly and with little effort. Even though demand for changeable production exists for some time, the practical application is still insufficient.

To overcome this deficit, a three year research project at the Department of Production Systems and Logistics at the Leibniz University of Hanover/ Germany was initiated. As a result of this project, different concepts have been developed to design production changeable. An excerpt of the results will be presented in this paper. An eight step procedure will be presented to design the changeability of production logistics. This procedure has been applied at a German manufacturer of high demanding weighing machines. The developed procedure, their application in industry, as well as the major results of the application will be presented.

Keywords: Changeability, Change Drivers, Production Logistics.

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Authors: Sushovan Sarkar, Debabrata Mazumder

Abstract:

Solid waste management in steel industry is broadly classified in “4 Rs” i.e. reduce, reuse, recycle and restore the materials. Reuse and recycling the entire solid waste generated in the process of steel making is a viable solution in targeting a clean, green and zero waste technology leading to sustainable development of the steel industry. Solid waste management has gained importance in steel industry in view of its uncertainty, volatility and speculation due to world competitive standards, rising input costs, scarcity of raw materials and solid waste generated like in other sectors. The challenges that the steel Industry faces today are the requirement of a sustainable development by meeting the needs of our present generation without compromising the ability of future generations. Technologies are developed not only for gainful utilization of solid wastes in manufacture of conventional products but also for conversion of same in to completely new products.

Keywords: Reuse, recycle, solid waste, sustainable development.

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Authors: Y. Bhatt, N. Ghosh, N. Tiwari

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Acreage response function are modeled taking account of expected harvest prices, weather related variables and other non-price variables allowing for partial adjustment possibility. At the outset, based on the literature on price expectation formation, we explored suitable formulations for estimating the farmer’s expected prices. Assuming that farmers form expectations rationally, the prices of food and biofuel crops are modeled using time-series methods for possible ARCH/GARCH effects to account for volatility. The prices projected on the basis of the models are then inserted to proxy for the expected prices in the acreage response functions. Food crop acreages in different growing states are found sensitive to their prices relative to those of one or more of the biofuel crops considered. The required percentage improvement in food crop yields is worked to offset the acreage loss.

Keywords: Acreage response function, biofuel, food security, sustainable development.

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Authors: Feddaoui Amina

Abstract:

Income smoothing represents an attempt on the part of the company's management to reduce variations in earnings through the manipulation of the accounting principles. In this study, we aimed to measure income smoothing practices in a sample of 30 French joint stock companies during the period (2007-2009), we used Dummy variables method and “ECKEL” model to measure income smoothing practices and Binomial test accourding to SPSS program, to confirm or refute our hypothesis. This study concluded that there are no significant statistical indicators of income smoothing practices in the sample studied of French companies during the period (2007-2009), so the income series in the same sample studied of is characterized by stability and non-volatility without any intervention of management through accounting manipulation. However, this type of accounting manipulation should be taken into account and efforts should be made by control bodies to apply Eckel model and generalize its use at the global level.

Keywords: Income, smoothing, “Eckel”, French companies.

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Authors: Dany Ng Cheong Vee, Preethee Nunkoo Gonpot, Noor-Ul-Hacq Sookia

Abstract:

In this paper, we consider the application of Extreme Value Theory as a risk measurement tool. The Value at Risk, for a set of indices, from six Stock Exchanges of Frontier markets is calculated using the Peaks over Threshold method and the performance of the model index-wise is evaluated using coverage tests and loss functions. Our results show that “fattailedness” alone of the data is not enough to justify the use of EVT as a VaR approach. The structure of the returns dynamics is also a determining factor. This approach works fine in markets which have had extremes occurring in the past thus making the model capable of coping with extremes coming up (Colombo, Tunisia and Zagreb Stock Exchanges). On the other hand, we find that indices with lower past than present volatility fail to adequately deal with future extremes (Mauritius and Kazakhstan). We also conclude that using EVT alone produces quite static VaR figures not reflecting the actual dynamics of the data.

Keywords: Extreme Value theory, Financial Crisis 2008, Frontier Markets, Value at Risk.

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Authors: Ichihan Tai, Bill Olson, Paul Blessner

Abstract:

Traditional early warning systems that alarm against crisis are generally based on structured or numerical data; therefore, a system that can make predictions based on unstructured textual data, an uncorrelated data source, is a great complement to the traditional early warning systems. The Chicago Board Options Exchange (CBOE) Volatility Index (VIX), commonly referred to as the fear index, measures the cost of insurance against market crash, and spikes in the event of crisis. In this study, news data is consumed for prediction of whether there will be a market-wide crisis by predicting the movement of the fear index, and the historical references to similar events are presented in an unsupervised manner. Topic modeling-based prediction and representation are made based on daily news data between 1990 and 2015 from The Wall Street Journal against VIX index data from CBOE.

Keywords: Early Warning System, Knowledge Management, Topic Modeling, Market Prediction.

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Authors: Petr Teply

Abstract:

The New Basel Capital Accord (Basel II) influences how financial institutions around the world, and especially European Union institutions, determine the amount of capital to reserve. However, as the recent global crisis has shown, the revision of Basel II is needed to reflect current trends, such as increased volatility and correlation, in the world financial markets. The overall objective of Basel II is to increase the safety and soundness of the international financial system. Basel II builds on three main pillars: Pillar I deals with the minimum capital requirements for credit, market and operational risk, Pillar II focuses on the supervisory review process and finally Pillar III promotes market discipline through enhanced disclosure requirements for banks. The aim of this paper is to provide the historical background, key features and impact of Basel II on financial markets. Moreover, we discuss new proposals for international bank regulation (sometimes referred to as Basel III) which include requirements for higher quality, constituency and transparency of banks' capital and risk management, regulation of OTC markets and introduction of new liquidity standards for internationally active banks.

Keywords: Basel II, Basel III, risk management, bank regulation

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Authors: Nnamdi I. Nwulu, Shola G. Oroja

Abstract:

It has become crucial over the years for nations to improve their credit scoring methods and techniques in light of the increasing volatility of the global economy. Statistical methods or tools have been the favoured means for this; however artificial intelligence or soft computing based techniques are becoming increasingly preferred due to their proficient and precise nature and relative simplicity. This work presents a comparison between Support Vector Machines and Artificial Neural Networks two popular soft computing models when applied to credit scoring. Amidst the different criteria-s that can be used for comparisons; accuracy, computational complexity and processing times are the selected criteria used to evaluate both models. Furthermore the German credit scoring dataset which is a real world dataset is used to train and test both developed models. Experimental results obtained from our study suggest that although both soft computing models could be used with a high degree of accuracy, Artificial Neural Networks deliver better results than Support Vector Machines.

Keywords: Artificial Neural Networks, Credit Scoring, SoftComputing Models, Support Vector Machines.

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Authors: Won-Hee Cho, GeunHyung Lee, Deok-Hwan Kim

Abstract:

The flash memory has many advantages such as low power consumption, strong shock resistance, fast I/O and non-volatility. And it is increasingly used in the mobile storage device. The YAFFS, one of the NAND flash file system, is widely used in the embedded device. However, the existing YAFFS takes long time to mount the file system because it scans whole spare areas in all pages of NAND flash memory. In order to solve this problem, we propose a new content-based flash file system using a mounting time reduction technique. The proposed method only scans partial spare areas of some special pages by using content-based block management. The experimental results show that the proposed method reduces the average mounting time by 87.2% comparing with JFFS2 and 69.9% comparing with YAFFS.

Keywords: NAND Flash Memory, Mounting Time, YAFFS, JFFS2, Content-based Block management

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Authors: Roopam Gaur, K. Chandramani Singh, Radhapiyari Laishram

Abstract:

In order to produce lead free piezoceramics with optimum piezoelectric and dielectric properties, KNN modified with Li+ (as an A site dopant) and Sb5+ (as a B site dopant) (K0.49Na0.49Li0.02) (Nb0.96Sb0.04) O3 (referred as KNLNS in this paper) have been synthesized using solid state reaction method and conventional sintering technique. The ceramics were sintered in the narrow range of 1050°C-1090°C for 2-3 h to get precise information about sintering parameters. Detailed study of dependence of microstructural, dielectric and piezoelectric properties on sintering conditions was then carried out. The study suggests that the volatility of the highly hygroscopic KNN ceramics is not only sensitive to sintering temperatures but also to sintering durations. By merely reducing the sintering duration for a given sintering temperature we saw an increase in the density of the samples which was supported by the increase in dielectric constants of the ceramics. And since density directly or indirectly affects almost all the associated properties, other dielectric and piezoelectric properties were also enhanced as we approached towards the most suitable sintering temperature and duration combination. The detailed results are reported in this paper.

Keywords: Piezoceramics, Conventional Sintering, KNN, Lead Free.

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Authors: N. Hatraf, L. Merabeti, Z. Neffeh, W. Taane

Abstract:

The excessive consumption of fossil energies (electrical energy) during summer caused by the technological development involves more and more climate warming.

In order to reduce the worst impact of gas emissions produced from classical air conditioning, heat driven solar absorption chiller is pretty promising; it consists on using solar as motive energy which is clean and environmentally friendly to provide cold.

Solar absorption machine is composed by four components using Lithium Bromide /water as a refrigerating couple. LiBr- water is the most promising in chiller applications due to high safety, high volatility ratio, high affinity, high stability and its high latent heat. The lithium bromide solution is constitute by the salt lithium bromide which absorbs water under certain conditions of pressure and temperature however if the concentration of the solution is high in the absorption chillers; which exceed 70%, the solution will crystallize.

The main aim of this article is to study the phenomena of the crystallization and to evaluate how the dependence between the electric conductivity and the concentration which should be controlled.

Keywords: Absorption chillers, crystallization, experimental results, Lithium Bromide solution.

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Authors: K. Jabeur, L. D. Buda-Prejbeanu, G. Prenat, G. Di Pendina

Abstract:

MRAM technology provides a combination of fast access time, non-volatility, data retention and endurance. While a growing interest is given to two-terminal Magnetic Tunnel Junctions (MTJ) based on Spin-Transfer Torque (STT) switching as the potential candidate for a universal memory, its reliability is dramatically decreased because of the common writing/reading path. Three-terminal MTJ based on Spin-Orbit Torque (SOT) approach revitalizes the hope of an ideal MRAM. It can overcome the reliability barrier encountered in current two-terminal MTJs by separating the reading and the writing path. In this paper, we study two possible writing schemes for the SOT-MTJ device based on recently fabricated samples. While the first is based on precessional switching, the second requires the presence of permanent magnetic field. Based on an accurate Verilog-A model, we simulate the two writing techniques and we highlight advantages and drawbacks of each one. Using the second technique, pioneering logic circuits based on the three-terminal architecture of the SOT-MTJ described in this work are under development with preliminary attractive results.

Keywords: Spin orbit Torque, Magnetic Tunnel Junction, MRAM, Spintronic, Circuit simulation.

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Authors: Peter Benneth, Tsaroh N. Theophilus, Prince Benjamin

Abstract:

This research work aims at studying the application of Legendre Transformation Method (LTM) to Hamilton Jacobi Bellman (HJB) equation which is an example of optimal control problem. We discuss the steps involved in modelling the HJB equation as it relates to mathematical finance by applying the Ito’s lemma and maximum principle theorem. By applying the LTM and dual theory, the resultant HJB equation is transformed to a linear Partial Differential Equation (PDE). Also, the Optimal Investment Strategy (OIS) and the optimal value function were obtained under the exponential utility function. Furthermore, some numerical results were also presented with observations that the OIS under exponential utility is directly proportional to the appreciation rate of the risky asset and inversely proportional to the instantaneous volatility, predetermined interest rate, risk averse coefficient. Finally, it was observed that the optimal fund size is an increasing function of the risk free interest rate. This result is consistent with some existing results.

Keywords: Legendre transformation method, Optimal investment strategy, Ito’s lemma, Hamilton Jacobi Bellman equation, Geometric Brownian motion, financial market.

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Authors: Edikan E. Akpanibah, Ogunmodimu Dupe Catherine

Abstract:

The relevance of geometric Brownian motion (GBM) in modelling the behaviour of stock market prices (SMP) cannot be over emphasized taking into consideration the volatility of the SMP. Consequently, there is need to investigate how GBM models are being estimated and used in financial market to predict SMP. To achieve this, the GBM estimation and its application to the SMP of some selected companies are studied. The normal and log-normal distributions were used to determine the expected value, variance and co-variance. Furthermore, the GBM model was used to predict the SMP of some selected companies over a period of time and the mean absolute percentage error (MAPE) were calculated and used to determine the accuracy of the GBM model in predicting the SMP of the four companies under consideration. It was observed that for all the four companies, their MAPE values were within the region of acceptance. Also, the MAPE values of our data were compared to an existing literature to test the accuracy of our prediction with respect to time of investment. Finally, some numerical simulations of the graphs of the SMP, expectations and variance of the four companies over a period of time were presented using MATLAB programming software.

Keywords: Stock Market, Geometric Brownian Motion, normal and log-normal distribution, mean absolute percentage error.

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