Search results for: 4/2 stochastic volatility model

Authors: Amirhossein Khazali, Mohsen Kalantar

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Energy storage units can play an important role to provide an economic and secure operation of future energy systems. In this paper, a stochastic energy and reserve market clearing scheme is presented considering storage energy units. The approach is proposed to deal with stochastic and non-dispatchable renewable sources with a high level of penetration in the energy system. A two stage stochastic programming scheme is formulated where in the first stage the energy market is cleared according to the forecasted amount of wind generation and demands and in the second stage the real time market is solved according to the assumed scenarios.

Keywords: energy and reserve market, energy storage device, stochastic programming, wind generation

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Babak Kamrani, Nozar Kishi

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Stochastic catalog represents the events module of the earthquake loss estimation models. It includes series of events with different magnitudes and corresponding frequencies/probabilities. For the development of the stochastic catalog, random or uniform sampling methods are used to sample the events from the seismicity model. For covering all the Magnitude Frequency Distribution (MFD), a huge number of events should be generated for the above-mentioned methods. Characteristic Event (CE) method chooses the events based on the interest of the insurance industry. We divide the MFD of each source into bins. We have chosen the bins based on the probability of the interest by the insurance industry. First, we have collected the information for the available seismic sources. Sources are divided into Fault sources, subduction, and events without specific fault source. We have developed the MFD for each of the individual and areal source based on the seismicity of the sources. Afterward, we have calculated the CE magnitudes based on the desired probability. To develop the stochastic catalog, we have introduced uncertainty to the location of the events too.

Keywords: stochastic catalogue, earthquake loss, uncertainty, characteristic event

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Authors: Faramarz Khosravi, Gokhan Izbirak

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A weighted statistical stochastic based Analytical Hierarchy Process (AHP) model for modeling the potential barriers and enablers of sustainability for measuring and assessing the sustainability level is proposed. For context-dependent potential barriers and enablers, the proposed model takes the basis of the properties of the variables describing the sustainability functions and was developed into a realistic analytical model for the sustainable behavior of an organization. This thus serves as a means for measuring the sustainability of the organization. The main focus of this paper was the application of the AHP tool in a statistically-based model for measuring sustainability. Hence a strong weighted stochastic AHP based procedure was achieved. A case study scenario of a widely reported major Canadian electric utility was adopted to demonstrate the applicability of the developed model and comparatively examined its results with those of an equal-weighted model method. Variations in the sustainability of a company, as fluctuations, were figured out during the time. In the results obtained, sustainability index for successive years changed form 73.12%, 79.02%, 74.31%, 76.65%, 80.49%, 79.81%, 79.83% to more exact values 73.32%, 77.72%, 76.76%, 79.41%, 81.93%, 79.72%, and 80,45% according to priorities of factors that have found by expert views, respectively. By obtaining relatively necessary informative measurement indicators, the model can practically and effectively evaluate the sustainability extent of any organization and also to determine fluctuations in the organization over time.

Keywords: AHP, sustainability fluctuation, environmental indicators, performance measurement

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Authors: Rancy Chepchirchir Kosgey, John Olukuru

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This study examines the impact of introduction of futures trading on the spot price volatility in the commodity market. The paper considers the United States of America, South Africa and Ethiopian economies. Three commodities i.e. coffee, maize and wheat from New York Merchantile Exchange, South African Futures Exchange and Ethiopian Commodity Exchange are analyzed. ARCH LM test is used to check for heteroskedasticity and GARCH and EGARCH are used to check for the behavior of volatility between the pre- and post-futures periods. For all the three economies, the results indicate presence of the ARCH effect in the log returns. For conditional and unconditional variances; spot price volatility for coffee has decreased after futures trading in all the economies and the EGARCH has also shown reduction in persistence of volatility in the post-futures period in the three economies; while that of maize has reduced for the Ethiopian economy while there has been an increase in both the US and South African economies. For wheat, the conditional variance has been found to rise in the post-futures period in all the three economies.

Keywords: derivatives, futures exchange, agricultural commodities, spot price volatility

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi

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This study was designed to find the best stochastic model (using of time series analysis) for annual extreme streamflow (peak and maximum streamflow) of Karkheh River at Iran. The Auto-regressive Integrated Moving Average (ARIMA) model used to simulate these series and forecast those in future. For the analysis, annual extreme streamflow data of Jelogir Majin station (above of Karkheh dam reservoir) for the years 1958–2005 were used. A visual inspection of the time plot gives a little increasing trend; therefore, series is not stationary. The stationarity observed in Auto-Correlation Function (ACF) and Partial Auto-Correlation Function (PACF) plots of annual extreme streamflow was removed using first order differencing (d=1) in order to the development of the ARIMA model. Interestingly, the ARIMA(4,1,1) model developed was found to be most suitable for simulating annual extreme streamflow for Karkheh River. The model was found to be appropriate to forecast ten years of annual extreme streamflow and assist decision makers to establish priorities for water demand. The Statistical Analysis System (SAS) and Statistical Package for the Social Sciences (SPSS) codes were used to determinate of the best model for this series.

Keywords: stochastic models, ARIMA, extreme streamflow, Karkheh river

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Authors: Mizan Ahmed, Srikanth Venkatesan

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Geological and tectonic framework indicates that Bangladesh is one of the most seismically active regions in the world. The Bengal Basin is at the junction of three major interacting plates: the Indian, Eurasian, and Burma Plates. Besides there are many active faults within the region, e.g. the large Dauki fault in the north. The country has experienced a number of destructive earthquakes due to the movement of these active faults. Current seismic provisions of Bangladesh are mostly based on earthquake data prior to the 1990. Given the record of earthquakes post 1990, there is a need to revisit the design provisions of the code. This paper compares the base shear demand of three major cities in Bangladesh: Dhaka (the capital city), Sylhet, and Chittagong for earthquake scenarios of magnitudes 7.0MW, 7.5MW, 8.0MW and 8.5MW using a stochastic model. In particular, the stochastic model allows the flexibility to input region specific parameters such as shear wave velocity profile (that were developed from Global Crustal Model CRUST2.0) and include the effects of attenuation as individual components. Effects of soil amplification were analysed using the Extended Component Attenuation Model (ECAM). Results show that the estimated base shear demand is higher in comparison with code provisions leading to the suggestion of additional seismic design consideration in the study regions.

Keywords: attenuation, earthquake, ground motion, Stochastic, seismic hazard

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Authors: Likewin Thomas, M. V. Manoj Kumar, B. Annappa

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The aim of this study was to develop an Artificial Neural Network0 s recommendation model for an online process using the complexity of load, performance, and average servicing time of the resources. Here, the proposed model investigates the resource performance using stochastic gradient decent method for learning ranking function. A probabilistic cost function is implemented to identify the optimal θ values (load) on each resource. Based on this result the recommendation of resource suitable for performing the currently executing task is made. The test result of CoSeLoG project is presented with an accuracy of 72.856%.

Keywords: ADALINE, neural network, gradient decent, process mining, resource behaviour, polynomial regression model

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Authors: Walid S. Alfuhaid, Saud A. Alghamdi, John M. Watkins, M. Edwin Sawan

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Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.

Keywords: decentralized, optimal control, output, singular perturb

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Authors: Tetsuji Tanaka, Jin Guo

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The extant literature has not succeeded in uncovering the common determinants of price volatility transmissions of agricultural commodities from international to local markets, and further, has rarely investigated the role of self-sufficiency measures in the context of national food security. We analyzed various factors to determine the degree of price volatility transmissions of wheat, rice, and maize between world and domestic markets using GARCH models with dynamic conditional correlation (DCC) specifications and panel-feasible generalized least square models. We found that the grain autarky system has the potential to diminish volatility pass-throughs for three grain commodities. Furthermore, it was discovered that the substitutive commodity consumption behavior between maize and wheat buffers the volatility transmissions of both, but rice does not function as a transmission-relieving element, either for the volatilities of wheat or maize. The effectiveness of grain consumption substitution to insulate the pass-throughs from global markets is greater than that of cereal self-sufficiency. These implications are extremely beneficial for developing governments to protect their domestic food markets from uncertainty in foreign countries and as such, improves food security.

Keywords: food security, GARCH, grain self-sufficiency, volatility transmission

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Authors: A. Y. Mukhtar, J. B. Munyakazi, R. Ouifki

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Over the past few decades, the unprecedented increase in mobility has raised considerable concern about the relationship between mobility and vector-borne diseases and malaria in particular. Thus, one can claim that human mobility is one of the contributing factors to the resurgence of malaria. To assess human mobility on malaria burden among hosts, we formulate a movement-based model on a network of patches. We then extend human multi-group SEIAR deterministic epidemic models into a system of stochastic differential equations (SDEs). Our quantitative stochastic model which is expressed in terms of average rates of movement between compartments is fitted to time-series data (weekly malaria data of 2011 for each patch) using the maximum likelihood approach. Using the metapopulation (multi-group) model, we compute and analyze the basic reproduction number. The result shows that human movement is sufficient to preserve malaria disease firmness in the patches with the low transmission. With these results, we concluded that the sensitivity of malaria to the human mobility is turning to be greatly important over the implications of future malaria control in South Sudan.

Keywords: basic reproduction number, malaria, maximum likelihood, movement, stochastic model

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Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo

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Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.

Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation

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Authors: Othmane Zarhali, Cécilia Aubrun, Emmanuel Bacry, Jean-Philippe Bouchaud, Jean-François Muzy

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The Nested factor model was introduced by Bouchaud and al., where the asset return fluctuations are explained by common factors representing the market economic sectors and residuals (noises) sharing with the factors a common dominant volatility mode in addition to the idiosyncratic mode proper to each residual. This construction infers that the factors-residuals log volatilities are correlated. Here, we consider the case of a single factor where the only dominant common mode is a S-fbm process (introduced by Peng, Bacry and Muzy) with Hurst exponent H around 0.11 and the residuals having in addition to the previous common mode idiosyncratic components with Hurst exponents H around 0. The reason for considering this configuration is twofold: preserve the Nested factor model’s characteristics introduced by Bouchaud and al. and propose a framework through which the stylized fact reported by Peng and al. is reproduced, where it has been observed that the Hurst exponents of stock indices are large as compared to those of individual stocks. In this work, we show that the Log S-fbm Nested factor model’s construction leads to a Hurst exponent of single stocks being the ones of the idiosyncratic volatility modes and the Hurst exponent of the index being the one of the common volatility modes. Furthermore, we propose a statistical procedure to estimate the Hurst factor exponent from the stock returns dynamics together with theoretical guarantees, with good results in the limit where the number of stocks N goes to infinity. Last but not least, we show that the factor can be seen as an index constructed from the single stocks weighted by specific coefficients.

Keywords: hurst exponent, log S-fbm model, nested factor model, small intermittency approximation

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Authors: Nadarajah I. Ramesh

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Much of the research on stochastic point process models for rainfall has focused on Poisson cluster models constructed from either the Neyman-Scott or Bartlett-Lewis processes. The doubly stochastic Poisson process provides a rich class of point process models, especially for fine-scale rainfall modelling. This paper provides an account of recent development on this topic and presents the results based on some of the fine-scale rainfall models constructed from this class of stochastic point processes. Amongst the literature on stochastic models for rainfall, greater emphasis has been placed on modelling rainfall data recorded at hourly or daily aggregation levels. Stochastic models for sub-hourly rainfall are equally important, as there is a need to reproduce rainfall time series at fine temporal resolutions in some hydrological applications. For example, the study of climate change impacts on hydrology and water management initiatives requires the availability of data at fine temporal resolutions. One approach to generating such rainfall data relies on the combination of an hourly stochastic rainfall simulator, together with a disaggregator making use of downscaling techniques. Recent work on this topic adopted a different approach by developing specialist stochastic point process models for fine-scale rainfall aimed at generating synthetic precipitation time series directly from the proposed stochastic model. One strand of this approach focused on developing a class of doubly stochastic Poisson process (DSPP) models for fine-scale rainfall to analyse data collected in the form of rainfall bucket tip time series. In this context, the arrival pattern of rain gauge bucket tip times N(t) is viewed as a DSPP whose rate of occurrence varies according to an unobserved finite state irreducible Markov process X(t). Since the likelihood function of this process can be obtained, by conditioning on the underlying Markov process X(t), the models were fitted with maximum likelihood methods. The proposed models were applied directly to the raw data collected by tipping-bucket rain gauges, thus avoiding the need to convert tip-times to rainfall depths prior to fitting the models. One advantage of this approach was that the use of maximum likelihood methods enables a more straightforward estimation of parameter uncertainty and comparison of sub-models of interest. Another strand of this approach employed the DSPP model for the arrivals of rain cells and attached a pulse or a cluster of pulses to each rain cell. Different mechanisms for the pattern of the pulse process were used to construct variants of this model. We present the results of these models when they were fitted to hourly and sub-hourly rainfall data. The results of our analysis suggest that the proposed class of stochastic models is capable of reproducing the fine-scale structure of the rainfall process, and hence provides a useful tool in hydrological modelling.

Keywords: fine-scale rainfall, maximum likelihood, point process, stochastic model

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Authors: Sasiwimol Auepong, Raywat Tanadkithirun

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In this work, the problem that squirrels ruin durian, which is an economical fruit in Thailand, is considered. We seek the strategy for the durian farmers to eliminate the squirrels under the consideration that squirrels also provide ecosystem service. The population dynamics of squirrels are constructed to have carrying capacity since we consider the population in a confined area. A performance index indicating the total benefit of a given elimination strategy is provided. It comprises the cost of countermeasures, the loss of resources, and the ecosystem service provided by squirrels. The optimal performance index is numerically solved through the variational inequality using the finite difference method. The optimal strategy to control the squirrel population is also given numerically.

Keywords: controlled stochastic differential equation, durian, finite difference method, performance index, singular stochastic control model, squirrel

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Authors: Montserrat Guillen, Stephania Mosquera-Lopez, Jorge Uribe

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An empirical study of market risk transmission between electricity prices in the Nord Pool interconnected market is done. Crucially, it is differentiated between risk propagation in the two tails of the price variation distribution. Thus, the downside risk from upside risk spillovers is distinguished. The results found document an asymmetric nature of risk and risk propagation in the two tails of the electricity price log variations. Risk spillovers following price increments in the market are transmitted to a larger extent than those after price reductions. Also, asymmetries related to both, the size of the transaction area and related to whether a given area behaves as a net-exporter or net-importer of electricity, are documented. For instance, on the one hand, the bigger the area of the transaction, the smaller the size of the volatility shocks that it receives. On the other hand, exporters of electricity, alongside countries with a significant dependence on renewable sources, tend to be net-transmitters of volatility to the rest of the system. Additionally, insights on the predictive power of positive and negative semivariances for future market volatility are provided. It is shown that depending on the forecasting horizon, downside and upside shocks to the market are featured by a distinctive persistence, and that upside volatility impacts more on net-importers of electricity, while the opposite holds for net-exporters.

Keywords: electricity prices, realized volatility, semivariances, volatility spillovers

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Authors: Reza Zakerinejad

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Gully erosion is a serious problem that threading the sustainability of agricultural area and rangeland and water in a large part of Iran. This type of water erosion is the main source of sedimentation in many catchment areas in the north of Iran. Since in many national assessment approaches just qualitative models were applied the aim of this study is to predict the spatial distribution of gully erosion processes by means of detail terrain analysis and GIS -based logistic regression in the loess deposition in a case study in the Golestan Province. This study the DEM with 25 meter result ion from ASTER data has been used. The Landsat ETM data have been used to mapping of land use. The TreeNet model as a stochastic modeling was applied to prediction the susceptible area for gully erosion. In this model ROC we have set 20 % of data as learning and 20 % as learning data. Therefore, applying the GIS and satellite image analysis techniques has been used to derive the input information for these stochastic models. The result of this study showed a high accurate map of potential for gully erosion.

Keywords: TreeNet model, terrain analysis, Golestan Province, Iran

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Authors: Mary Chriselda A

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This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

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Authors: Michael Fundator

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Groundbreaking application of biomathematical and biochemical research in neural networks processes to formation of non-canonical bases, islands, and analog bases in DNA and mRNA at or near the transcription that contradicts the long anticipated statistical assumptions for the distribution of bases and analog bases compounds is implemented through statistical and stochastic methods apparatus with addition of quantum principles, where the usual transience of Poisson spike train becomes very instrumental tool for finding even almost periodical type of solutions to Fokker-Plank stochastic differential equation. Present article develops new multidimensional methods of finding solutions to stochastic differential equations based on more rigorous approach to mathematical apparatus through Kolmogorov-Chentsov continuity theorem that allows the stochastic processes with jumps under certain conditions to have γ-Holder continuous modification that is used as basis for finding analogous parallels in dynamics of neutral networks and formation of analog bases and transcription in DNA.

Keywords: Fokker-Plank stochastic differential equation, Kolmogorov-Chentsov continuity theorem, neural networks, translation and transcription

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Authors: Aida Alemany, Laura Ballester, Ana González-Urteaga

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From 2007 subprime crisis to the recent Eurozone debt crisis the European banking industry has experienced a terrible financial instability situation with increasing levels of CDS spreads (used as a proxy of credit risk). This paper investigates whether volatility transmission channels in European banking markets have changed after three significant crises’ events during the period January 2006 to March 2013. The global financial crisis is characterized by a unidirectional volatility shocks spillovers effect in credit risk from inside to outside the Eurozone. By contrast, the Eurozone debt crisis is revealed to be local in nature with the euro as the key element suggesting a market fragmentation between distressed peripheral and non-distressed core Eurozone countries, whereas retaining the local currency have acted as a firewall. With these findings we are able to shed light on the impact of the different crises on the European banking credit risk dynamics.

Keywords: CDS spreads, credit risk, volatility spillovers, financial crisis

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Authors: Ezgi Nevruz, Kasirga Yildirak, Ashis SenGupta

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Comparing or ranking risks is the main motivating factor behind the human trait of making choices. Cumulative prospect theory (CPT) is a preference theory approach that evaluates perception and bias in decision making under risk and uncertainty. We aim to investigate the aggregate claims of different risk classes in terms of their comparability and amenability to ordering when the impact of risk perception is considered. For this aim, we prioritize the aggregate claims taken as actuarial risks by using various stochastic ordering relations. In order to prioritize actuarial risks, we use stochastic relations such as stochastic dominance and stop-loss dominance that are proposed in the frame of partial order theory. We take into account the dependency of the individual claims exposed to similar environmental risks. At first, we modify the zero-utility premium principle in order to obtain a solution for the stop-loss premium under CPT. Then, we propose a stochastic stop-loss dominance of the aggregate claims and find a relation between the stop-loss dominance and the first-order stochastic dominance under the dependence assumption by using properties of the familiar as well as some emerging multivariate claim distributions.

Keywords: cumulative prospect theory, partial order theory, risk perception, stochastic dominance, stop-loss dominance

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Authors: Yegnanew A. Shiferaw

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Background: commodity price volatility originating from excessive commodity price fluctuation has been a global problem especially after the recent financial crises. Volatility is a measure of risk or uncertainty in financial analysis. It plays a vital role in risk management, portfolio management, and pricing equity. Objectives: the core objective of this paper is to examine the relationship between the prices of agricultural commodities with oil price, gas price, coal price and exchange rate (USD/Rand). In addition, the paper tries to fit an appropriate model that best describes the log return price volatility and estimate Value-at-Risk and expected shortfall. Data and methods: the data used in this study are the daily returns of agricultural commodity prices from 02 January 2007 to 31st October 2016. The data sets consists of the daily returns of agricultural commodity prices namely: white maize, yellow maize, wheat, sunflower, soya, corn, and sorghum. The paper applies the three-state Markov-switching (MS) regression, the standard single-regime GARCH and the two regime Markov-switching GARCH (MS-GARCH) models. Results: to choose the best fit model, the log-likelihood function, Akaike information criterion (AIC), Bayesian information criterion (BIC) and deviance information criterion (DIC) are employed under three distributions for innovations. The results indicate that: (i) the price of agricultural commodities was found to be significantly associated with the price of coal, price of natural gas, price of oil and exchange rate, (ii) for all agricultural commodities except sunflower, k=3 had higher log-likelihood values and lower AIC and BIC values. Thus, the three-state MS regression model outperformed the two-state MS regression model (iii) MS-GARCH(1,1) with generalized error distribution (ged) innovation performs best for white maize and yellow maize; MS-GARCH(1,1) with student-t distribution (std) innovation performs better for sorghum; MS-gjrGARCH(1,1) with ged innovation performs better for wheat, sunflower and soya and MS-GARCH(1,1) with std innovation performs better for corn. In conclusion, this paper provided a practical guide for modelling agricultural commodity prices by MS regression and MS-GARCH processes. This paper can be good as a reference when facing modelling agricultural commodity price problems.

Keywords: commodity prices, MS-GARCH model, MS regression model, South Africa, volatility

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Authors: Vinayak Bassi, Rajpreet Singh

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Over the years, with the emergence of sophisticated computers and algorithms, finance has been quantified using computational prowess. Asset valuation has been one of the key components of quantitative finance. In fact, it has become one of the embryonic steps in determining risk related to a portfolio, the main goal of quantitative finance. This study comprises a drawing comparison between valuation output generated by two stochastic dynamic models, namely Black-Scholes and Dupire’s bi-dimensionality model. Both of these models are formulated for computing the valuation function for a portfolio of European options using Monte Carlo simulation methods. Although Monte Carlo algorithms have a slower convergence rate than calculus-based simulation techniques (like FDM), they work quite effectively over high-dimensional dynamic models. A fidelity gap is analyzed between the static (historical) and stochastic inputs for a sample portfolio of underlying assets. In order to enhance the performance efficiency of the model, the study emphasized the use of variable reduction methods and customizing random number generators to implement parallelization. An attempt has been made to further implement the Dupire’s model on a GPU to achieve higher computational performance. Furthermore, ideas have been discussed around the performance enhancement and bottleneck identification related to the implementation of options-pricing models on GPUs.

Keywords: monte carlo, stochastic models, computational finance, parallel programming, scientific computing

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Authors: Abderrazek Ben Maatoug, Ibrahim Fatnassi, Wassim Ben Ayed

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In this paper we investigate the issue of market risk quantification for Middle East and North Africa (MENA) Islamic market equity. We use Value-at-Risk (VaR) as a measure of potential risk in Islamic stock market, for long and short position, based on Riskmetrics model and the conditional parametric ARCH class model volatility with normal, student and skewed student distribution. The sample consist of daily data for the 2006-2014 of 11 Islamic stock markets indices. We conduct Kupiec and Engle and Manganelli tests to evaluate the performance for each model. The main finding of our empirical results show that (i) the superior performance of VaR models based on the Student and skewed Student distribution, for the significance level of α=1% , for all Islamic stock market indices, and for both long and short trading positions (ii) Risk Metrics model, and VaR model based on conditional volatility with normal distribution provides the best accurate VaR estimations for both long and short trading positions for a significance level of α=5%.

Keywords: value-at-risk, risk management, islamic finance, GARCH models

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Authors: Mojtaba Aghamiri Esfahani, Mohammad Karkon, Seyed Majid Hosseini Nezhad, Reza Hosseini-Ara

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In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords: stochastic finite elements, plate bending, free vibration, Monte Carlo, Neumann expansion method.

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Authors: Keerthi S. Shetty, Annappa Basava

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In recent years, modelling of biological systems represented by biochemical reactions has become increasingly important in Systems Biology. Biological systems represented by biochemical reactions are highly stochastic in nature. Probabilistic model is often used to describe such systems. One of the main challenges in Systems biology is to combine absolute experimental data into probabilistic model. This challenge arises because (1) some molecules may be present in relatively small quantities, (2) there is a switching between individual elements present in the system, and (3) the process is inherently stochastic on the level at which observations are made. In this paper, we describe a novel idea of combining absolute experimental data into probabilistic model using tool R2. Through a case study of the Transcription Process in Prokaryotes we explain how biological systems can be written as probabilistic program to combine experimental data into the model. The model developed is then analysed in terms of intrinsic noise and exact sampling of switching times between individual elements in the system. We have mainly concentrated on inferring number of genes in ON and OFF states from experimental data.

Keywords: systems biology, probabilistic model, inference, biology, model

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Authors: Zahid Ahmad, Nosheen Imran, Nauman Ali, Farah Amir

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The objective of the study is to forecast the US Dollar and Pak Rupee exchange rate by using time series models. For this purpose, daily exchange rates of US and Pakistan for the period of January 01, 2007 - June 2, 2017, are employed. The data set is divided into in sample and out of sample data set where in-sample data are used to estimate as well as forecast the models, whereas out-of-sample data set is exercised to forecast the exchange rate. The ADF test and PP test are used to make the time series stationary. To forecast the exchange rate ARIMA model and GARCH model are applied. Among the different Autoregressive Integrated Moving Average (ARIMA) models best model is selected on the basis of selection criteria. Due to the volatility clustering and ARCH effect the GARCH (1, 1) is also applied. Results of analysis showed that ARIMA (0, 1, 1 ) and GARCH (1, 1) are the most suitable models to forecast the future exchange rate. Further the GARCH (1,1) model provided the volatility with non-constant conditional variance in the exchange rate with good forecasting performance. This study is very useful for researchers, policymakers, and businesses for making decisions through accurate and timely forecasting of the exchange rate and helps them in devising their policies.

Keywords: exchange rate, ARIMA, GARCH, PAK/USD

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi, Abdolrasoul Telvari, Hossein Babazadeh

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Floods have huge environmental and economic impact. Therefore, flood prediction is given a lot of attention due to its importance. This study analysed the annual maximum streamflow (discharge) (AMS or AMD) of Karkheh River in Karkheh River Basin for flood predicting using ARIMA model. For this purpose, we use the Box-Jenkins approach, which contains four-stage method model identification, parameter estimation, diagnostic checking and forecasting (predicting). The main tool used in ARIMA modelling was the SAS and SPSS software. Model identification was done by visual inspection on the ACF and PACF. SAS software computed the model parameters using the ML, CLS and ULS methods. The diagnostic checking tests, AIC criterion, RACF graph and RPACF graphs, were used for selected model verification. In this study, the best ARIMA models for Annual Maximum Discharge (AMD) time series was (4,1,1) with their AIC value of 88.87. The RACF and RPACF showed residuals’ independence. To forecast AMD for 10 future years, this model showed the ability of the model to predict floods of the river under study in the Karkheh River Basin. Model accuracy was checked by comparing the predicted and observation series by using coefficient of determination (R²).

Keywords: time series modelling, stochastic processes, ARIMA model, Karkheh river

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Authors: Chi Zhang, Hua-Peng Chen

Abstract:

With the increasingly demanding resources in the word, renewable and clean energy has been considered as an alternative way to replace traditional ones. Thus, one of practical examples for using wind energy is wind turbine, which has gained more attentions in recent research. Like most offshore structures, the blades, which is the most critical components of the wind turbine, will be subjected to millions of loading cycles during service life. To operate safely in marine environments, the blades are typically made from fibre reinforced composite materials to resist fatigue delamination and harsh environment. The fatigue crack development of blades is uncertain because of indeterminate mechanical properties for composite and uncertainties under offshore environment like wave loads, wind loads, and humid environments. There are three main delamination failure modes for composite blades, and the most common failure type in practices is subjected to mixed mode loading, typically a range of opening (mode 1) and shear (mode 2). However, the fatigue crack development for mixed mode cannot be predicted as deterministic values because of various uncertainties in realistic practical situation. Therefore, selecting an effective stochastic model to evaluate the mixed mode behaviour of wind turbine blades is a critical issue. In previous studies, gamma process has been considered as an appropriate stochastic approach, which simulates the stochastic deterioration process to proceed in one direction such as realistic situation for fatigue damage failure of wind turbine blades. On the basis of existing studies, various Paris Law equations are discussed to simulate the propagation of the fatigue crack growth. This paper develops a Paris model with the stochastic deterioration modelling according to gamma process for predicting fatigue crack performance in design service life. A numerical example of wind turbine composite materials is investigated to predict the mixed mode crack depth by Paris law and the probability of fatigue failure by gamma process. The probability of failure curves under different situations are obtained from the stochastic deterioration model for comparisons. Compared with the results from experiments, the gamma process can take the uncertain values into consideration for crack propagation of mixed mode, and the stochastic deterioration process shows a better agree well with realistic crack process for composite blades. Finally, according to the predicted results from gamma stochastic model, assessment strategies for composite blades are developed to reduce total lifecycle costs and increase resistance for fatigue crack growth.

Keywords: Reinforced fibre composite, Wind turbine blades, Fatigue delamination, Mixed failure mode, Stochastic process.

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Authors: Ons Triki, Fathi Abid

Abstract:

Along with the increase in the use of leasing contracts in corporate finance, multiple studies aim to model the credit risk of the lease in order to cover the losses of the lessor of the asset if the lessee goes bankrupt. In the current research paper, a convertible lease contract is elaborated in a continuous time stochastic universe aiming to ensure the financial stability of the firm and quickly recover the losses of the counterparties to the lease in case of default. This work examines the term structure of the lease rates taking into account the credit default risk and the capital structure of the firm. The interaction between the lessee's capital structure and the equilibrium lease rate has been assessed by applying the competitive lease market argument developed by Grenadier (1996) and the endogenous structural default model set forward by Leland and Toft (1996). The cumulative probability of default was calculated by referring to Leland and Toft (1996) and Yildirim and Huan (2006). Additionally, the link between lessee credit risk and lease rate was addressed so as to explore the impact of convertible lease financing on the term structure of the lease rate, the optimal leverage ratio, the cumulative default probability, and the optimal firm value by applying an endogenous conversion threshold. The numerical analysis is suggestive that the duration structure of lease rates increases with the increase in the degree of the market price of risk. The maximal value of the firm decreases with the effect of the optimal leverage ratio. The results are indicative that the cumulative probability of default increases with the maturity of the lease contract if the volatility of the asset service flows is significant. Introducing the convertible lease contract will increase the optimal value of the firm as a function of asset volatility for a high initial service flow level and a conversion ratio close to 1.

Keywords: convertible lease contract, lease rate, credit-risk, capital structure, default probability

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