• Journal of applied mathematics & informatics
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• 제41권1호
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• pp.33-50
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• 2023

Foreign exchange options are derivative financial instruments that can exchange one currency for another at a prescribed exchange rate on a specified date. In this study, we examine the analytic formulas for vulnerable foreign exchange options based on multi-scale stochastic volatility driven by two diffusion processes: a fast mean-reverting process and a slow mean-reverting process. In particular, we take advantage of the asymptotic analysis and the technique of the Mellin transform on the partial differential equation (PDE) with respect to the option price, to derive approximated prices that are combined with a leading order price and two correction term prices. To verify the price accuracy of the approximated solutions, we utilize the Monte Carlo method. Furthermore, in the numerical experiments, we investigate the behaviors of the vulnerable foreign exchange options prices in terms of model parameters and the sensitivities of the stochastic volatility factors to the option price.

• Structural Engineering and Mechanics
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• 제15권4호
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• pp.381-394
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• 2003

While constructing multistorey buildings with reinforced concrete framed structures it is a common practice to provide parking space for vehicles at the ground floor level. This floor will generally consist of open frames without any infilled walls and is called an open-storey. From a post disaster damage survey carried out, it was noticed that during the January 26, 2001 Bhuj (Gujarat, India) earthquake, a large number of reinforced concrete framed buildings with open-storey at ground floor level, suffered extensive damage and in some cases catastrophic collapse. This has brought into sharp focus the need to carry out systematic studies on the seismic vulnerability of such buildings. Determination of vulnerability requires realistic structural response estimations taking into account the stochasticity in the loading and the system parameters. The stochastic finite element method can be effectively used to model the random fields while carrying out such studies. This paper presents the details of stochastic finite element analysis of a five-storey three-bay reinforced concrete framed structure with open-storey subjected to standard seismic excitation. In the present study, only the stochasticity in the system parameters is considered. The stochastic finite element method used for carrying out the analysis is based on perturbation technique. Each random field representing the stochastic geometry/material property is discretised into correlated random variables using spatial averaging technique. The uncertainties in geometry and material properties are modelled using the first two moments of the corresponding parameters. In evaluating the stochastic response, the cross-sectional area and Young' modulus are considered as independent random fields. To study the influence of correlation length of random fields, different correlation lengths are considered for random field discretisation. The spatial expectations and covariances for displacement response at any time instant are obtained as the output. The effect of open-storey is modelled by suitably considering the stiffness of infilled walls in the upper storey using cross bracing. In order to account for changes in soil conditions during strong motion earthquakes, both fixed and hinged supports are considered. The results of the stochastic finite element based seismic analysis of reinforced concrete framed structures reported in this paper demonstrate the importance of considering the effect of open-storey with appropriate support conditions to estimate the realistic response of buildings subjected to earthquakes.

• 전산구조공학
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• 제5권1호
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• pp.97-108
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• 1992

이 논문에서는 구조시스템신뢰성해석에 있어서 부재의 파괴후 잔류강도의 불확실성을 고려하였다. 이를 위하여 확율유한요소법(Stochastic Finite Element Method: SFEM)을 시스템신뢰성해석과정에 접합하였다. 확율유한요소법은 신뢰성해석시 재료와 기하학적 변수의 불확실성을 좀더 함축적으로 고려할 수 있는 것으로 알려져 있으며, 본 논문에서 이 방법을 구조부재와 구조시스템의 신뢰성해석에 적용해 보았다. 이 논문의 방법과 파괴된 부재의 잔류응력을 확정적으로 취급하는 방법과 그 결과를 비교하였으며, 부재가 파괴된 후 그 잔류강도의 불확실성이 구조시스템 신뢰성에 주는 영향을 보기위해 여러 경우를 고찰해 보았다. 그 결과로부터 부재의 파괴 후 잔류강도가 구조시스템신뢰성에 대단히 큰 영향을 준다는 것을 다시 확인할 수 있었다. 이 논문의 여러경우에 대한 연구로 부터 좀 더 나은 구조시스템신뢰성의 평가를 위해서 부재의 파괴후 거동이 갖는 불확실성을 구조시스템신뢰성해석시, 특히 부재의 파괴후 거동이 semi-brittle인 경우에, 고려해야 한다는 결론을 내릴 수 있겠다. 이점을 받아들인다면 확율유한요소법이 구조시스템신뢰성해석에 있어서 적합한 방법일 것이다.

• 경영과학
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• 제19권1호
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• pp.117-128
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• 2002

In this Paper we investigate the performance of the five efficiency estimation methods which include the stochastic frontier model estimated by maximum likelihood (SFML), the stochastic frontier model estimated by corrected ordinary least squares (SFCOLS), the data envelopment analysis (DIA) model, the combined estimation of SFML and DEA (SFML + DEA), and the combined estimation of SFCOLS arid DIA (SFCOLS+ DEA) using Monte Carlo analysis. The results include: 1) SFML provides most accurate efficiency estimates for the sample sloe 150 or over,2) SFML+DEAor SFCOLS + DIA Perform better for the cases with sample sloe 25, 50, and low random errors, 3) SFCOLS performs better for the close with sample sloe 25, 50, and very high random errors.

• Journal of Advanced Research in Ocean Engineering
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• 제1권1호
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• pp.55-62
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• 2015

Floating structure such as tension leg platform, semi-submersible and spar are widely used in field of oil exploration and renewable energy system. All of these structures have the base cylinder support structure which have effective rule in overall dynamic of response. So the accurate and reliable modeling is needed for optimum design and understanding the physical background of these systems. The aim of this article is an analytical discussion on stochastic modeling of floating cylinder based support structure but an applicable one. Due to this a mathematical mass-damper-spring system of a floating cylinder of HAWAII WTG offshore wind as an applicable and innovative system is adopted to model a coupled degrees using random vibration in analytical way. A fully develop spectrum is adopted to solve the stochastic spectrum analytically by a proper approximation. Some acceptable assumption is adopted. The simplified but analytical and innovative hydrodynamic analysis of this study not only will help researcher to concentrate more physically on hydrodynamic analysis of floating structures but also can be useful for any quick, simplified and closed form analysis of a complicated problem in offshore engineering.

• 한국터널지하공간학회 논문집
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• 제12권3호
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• pp.265-274
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• 2010

터널에서 암반구조의 복잡성으로 인해 사전에 예측 할 수 없었던 암반의 붕락이 발생하여, 붕락대책에 막대한 비용과 시간을 낭비하는 사례가 많다. 암반 불연속면의 복잡성을 사전 조사 단계에서 충분히 파악하거나 대책을 수립하는 것은 어렵다. 최근 터널의 정보화 설계시공이 중요시 되어지고 있다. 본 연구에서는 터널의 굴착 전에 관찰된 정보를 최대한 활용하여 불안정한 암반블럭을 사전에 예측하기 위하여 신 하이브리드 추계학적-확정론적 암반블럭 해석기법을 제안하고, 현지에서 관찰한 불연속면 정보를 근거로 하여 터널현장에 적용했다. 터널현장에서의 해석결과를 비교 검토하여, 터널의 신 하이브리드 추계학적-확정론적 암반블럭 해석기법의 타당성과 적용성에 대한 검증을 하였다.

• Wind and Structures
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• 제18권6호
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• pp.693-715
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• 2014

Stochastic processes are used to represent phenomena in many diverse fields. Numerical simulation method is widely applied for the solution to stochastic problems of complex structures when alternative analytical methods are not applicable. In some practical applications the stochastic processes show non-Gaussian properties. When the stochastic processes deviate significantly from Gaussian, techniques for their accurate simulation must be available. The various existing simulation methods of non-Gaussian stochastic processes generally can only simulate super-Gaussian stochastic processes with the high-peak characteristics. And these methodologies are usually complicated and time consuming, not sufficiently intuitive. By revealing the inherent coupling effect of the phase and amplitude part of discrete Fourier representation of random time series on the non-Gaussian features (such as skewness and kurtosis) through theoretical analysis and simulation experiments, this paper presents a novel approach for the simulation of non-Gaussian stochastic processes with the prescribed amplitude probability density function (PDF) and power spectral density (PSD) by amplitude modulation and phase reconstruction. As compared to previous spectral representation method using phase modulation to obtain a non-Gaussian amplitude distribution, this non-Gaussian phase reconstruction strategy is more straightforward and efficient, capable of simulating both super-Gaussian and sub-Gaussian stochastic processes. Another attractive feature of the method is that the whole process can be implemented efficiently using the Fast Fourier Transform. Cases studies demonstrate the efficiency and accuracy of the proposed algorithm.

• Computers and Concrete
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• 제9권3호
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• pp.195-213
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• 2012

This paper presents the investigation of the stochastic responses of seismically isolated bridges subjected to spatially varying earthquake ground motions including incoherence, wave-passage and site-response effects. The incoherence effect is examined by considering Harichandran and Vanmarcke coherency model. The effect of the wave-passage is dealt with various wave velocities in the response analysis. Homogeneous firm, medium and soft soil conditions are selected for considering the site-response effect where the bridge supports are constructed. The ground motion is described by filtered white noise and applied to each support points. For seismic isolation of the bridge, single and double concave friction pendulum bearings are used. Due to presence of friction on the concave surfaces of the isolation systems, the equation of motion of is non-linear. The non-linear equation of motion is solved by using equivalent linearization technique of non-linear stochastic analyses. Solutions obtained from the stochastic analyses of non-isolated and isolated bridges to spatially varying earthquake ground motions compared with each other for the special cases of the ground motion model. It is concluded that friction pendulum systems having single and double concave surfaces have important effects on the stochastic responses of bridges to spatially varying earthquake ground motions.

• 한국정보통신학회논문지
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• 제18권11호
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• pp.2634-2639
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• 2014

시스템 및 네트워크의 안정적인 서비스를 위한 기본적인 구조로 다양한 이중화 방식이 있다. 또한 시스템 및 네트워크의 성능을 분석하기 위하여 페트리네트에서부터 Stochastic Reward Net(SRN)에 이르기까지 다양한 성능 분석 모형이 존재한다. 본 논문에서는 정상 상태에서 하나의 액티브 서비스 유닛과 하나의 스탠바이 서비스 유닛을 가진 2N 이중화 방식을 SRN으로 모형화 한다. 성능 분석 소프트웨어인 추계적 페트리네트 패키지 SPNP를 사용하여 2N 이중화 방식의 가용도를 분석한다.

• Structural Engineering and Mechanics
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• 제82권1호
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• pp.31-40
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• 2022

In structural engineering, the material properties of the structures such as elastic modulus, shear modulus, density, and size may not be deterministic and may vary at different locations. The dynamic response analysis of such structures may need to consider these properties as stochastic. This paper introduces a stochastic finite element method (SFEM) approach to analyze moving loads problems. Firstly, Karhunen-Loéve expansion (KLE) is applied for expressing the stochastic field of material properties. Then the mathematical expression of the random field is substituted into the finite element model to formulate the corresponding random matrix. Finally, the statistical moment of the dynamic response is calculated by the point estimation method (PEM). The accuracy and efficiency of the dynamic response obtained from the KLE-PEM are demonstrated by the example of a moving load passing through a simply supported Euler-Bernoulli beam, in which the material properties (including elastic modulus and density) are considered as random fields. The results from the KLE-PEM are compared with those from the Monte Carlo simulation. The results demonstrate that the proposed method of KLE-PEM has high accuracy and efficiency. By using the proposed SFEM, the random vertical deflection of a high-speed railway (HSR) bridge is analyzed by considering the random fields of material properties under the moving load of a train.