• 대한수학회보
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• 제48권4호
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• pp.791-812
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• 2011

This is a survey on American options. An American option allows its owner the privilege of early exercise, whereas a European option can be exercised only at expiration. Because of this early exercise privilege American option pricing involves an optimal stopping problem; the price of an American option is given as a free boundary value problem associated with a Black-Scholes type partial differential equation. Up until now there is no simple closed-form solution to the problem, but there have been a variety of approaches which contribute to the understanding of the properties of the price and the early exercise boundary. These approaches typically provide numerical or approximate analytic methods to find the price and the boundary. Topics included in this survey are early approaches(trees, finite difference schemes, and quasi-analytic methods), an analytic method of lines and randomization, a homotopy method, analytic approximation of early exercise boundaries, Monte Carlo methods, and relatively recent topics such as model uncertainty, backward stochastic differential equations, and real options. We also provide open problems whose answers are expected to contribute to American option pricing.

• 물과 미래
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• 제16권2호
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• pp.123-129
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• 1983

One of the techniques to determine flood stages in natural channel is to find the solution of unsteady flow equations such as continuity and momentum equations. Since the exact analytic solution of these equations are not Known, the implicit numerical scheme is widely accepted tool for the approximate solution of equations. This technique is applied to the downstream of Daechung Dam in Geum River for the determination of flood stage for given frequency. However the flood stages are greatly affected by the method of reservoir Operation Method and Technical Operation Reservoir Method. Obviously, the Tech. ROM is found to be superior to Auto ROM.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2005년도 추계 학술대회논문집
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• pp.183-186
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• 2005

We developed an upwind numerical formulation based on the eigenvalues of the approximate Jacobian matrix in order to solve the hyperbolic conservation laws governing the two-fluid two-phase flow models. We obtained eight analytic eigenvalues in the two dimensions that can be used for estimate of the wave speeds essential in constructing an upwind numerical method. Two-dimensional underwater cavitation in a flow past structural shapes or by underwater explosion can be solved using this method. We present quantitative prediction of cavitation for the water tunnel wall and airfoils that has both experimental data as well as numerical results by other numerical methods and models.

• International Journal of Naval Architecture and Ocean Engineering
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• 제4권3호
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• pp.267-280
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• 2012

An approximate method based on an assumed mode method has been presented for the free vibration analysis of a rectangular plate with arbitrary edge constraints. In the presented method, natural frequencies and their mode shapes of the plate are calculated by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. Characteristic orthogonal polynomials having the property of Timoshenko beam functions which satisfies edge constraints corresponding to those of the objective plate are used. In order to examine the accuracy of the proposed method, numerical examples of the rectangular plates with various thicknesses and edge constraints have been presented. The results have shown good agreement with those of other methods such as an analytic solution, an approximate solution, and a finite element analysis.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2006년도 추계 학술대회논문집
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• pp.97-100
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• 2006

An ejector is designed for the purpose of engine bay cooling and exhaust gas cooling. The primary flow of the ejector is the exhaust gas of the turboshaft engine. The mass flow of secondary flow is calculated by using the approximate analytic equation. For the purpose of verification of approximate method, comparison is made with the results of Navier-Stokes turbulent flow solution. According to the results of CFD, the mixing of two flows is incomplete due to the short length of mixing duct.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2005년도 춘계 학술대회논문집
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• pp.219-222
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• 2005

A compressible two-fluid two-phase flow computation model using the stiffened-gas equation of state is formulated. Since the conservation equation system is of mixed type, it gives complex eigenvalues. The sonic speeds obtained from the individual single phase have been simply used in the literature for the fastest wave speeds necessary in the HLL scheme. This method has worked fine but proved to be quite diffusive according to our test. To improve the accuracy, we here propose to utilize the analytic eigenvalues evaluated from an approximate Jacobian matrix lot the fastest wave speeds. The interfacial transfer terms were dropped in constituting the Jacobian matrix for this purpose. The present scheme proved efficient, robust and accurate in comparison with other existing methods. We solved the cavitating flow problem using the present scheme. The result shows more detailed wave structure in the cavitating process caused by the strong expansion waves.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2009년도 제7회 압연 심포지엄
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• pp.97-102
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• 2009

In hot strip rolling, sound prediction of the temperature of the strip is vital for achieving the desired finishing mill draft temperature (FDT). In this paper, a precision on-line model for the prediction of temperature distributions along the thickness of the strip in the finishing mill is presented. The model consists of an analytic model for the prediction of temperature distributions in the inter-stand zone, and a semi-analytic model for the prediction of temperature distributions in the bite zone in which thermal boundary conditions as well as heat generation due to deformation are predicted by finite element-based, approximate models. The prediction accuracy of the proposed model is examined through comparison with predictions from a finite element process model.

• International Journal of CAD/CAM
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• 제3권1_2호
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• pp.97-109
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• 2003

A large scale polygon models are often used to approximately represent 3D CAD models in Digital Engineering environment such as DMU (Digital Mockups) and network based collaborative design. However, they are not suitable for distribution on the network and for interactive rendering. We introduce a new coding system based on subdivision schemes called S-CODE system. In this system, it is possible to highly compress the model with sufficient accuracy and to view the model efficiently in a level of detail (LOD) fashion. The method is based on subdivision surface fitting by which a subdivision surface and curves which approximate a face of a CAD model are generated. We also apply a subdivision method to analytic surfaces such as conical and cylindrical surfaces. A prototype system is developed and used for evaluation with reasonably complicated data. The results show that the method is useful as a CAD data coding system.

• 대한조선학회논문집
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• 제35권1호
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• pp.1-14
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• 1998

2차원 천수방정식에 기초한 조류계산 수치모델을 개발하였다. 복잡한 해안선의 입력을 단순화할 수 있는 직각격자를 사용하였으며, 방정식은 효율이 뛰어난 것으로 알려져 있는 인수분해음해법(Implicit Factorization Method)에 의하여 수치적으로 풀었다. 대류항은 상류차분법으로 처리하여 수치소산이 자동적으로 들어가도록 하였으며, 따라서 수치불안정에 의한 발산을 억제할 수 있었다. 모델의 검증을 위하여 선형화된 천수방정식을 풀고 계산결과를 해석해와 비교하였으며 잘 일치하고 있음을 확인하였다. 수치모델의 응용 예로서 인천항부근의 경인운하 개발예정인 수로에서의 조류 계산결과를 보였다.

• Water Engineering Research
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• 제3권1호
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• pp.23-30
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• 2002

A numerical model for the solution of two-dimensional dam break problems using fractional step method is developed on unstructured grid. The model is based on second-order Weighted Averaged Flux(WAF) scheme with HLLC approximate Riemann solver. To control the nonphysical oscillations associated with second-order accuracy, TVD scheme with SUPERBEE limiter is used. The developed model is verified by comparing the computational solutions with analytic solutions in idealized test cases. Very good agreements have been achieved in the verifications.