• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.529-548
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• 2007

The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.937-942
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• 2009

In this paper, a continuous-time risk process in an insurance business is considered, where the premium rate is constant and the claim process forms a compound Poisson process. We say that a ruin occurs if the surplus of the risk process becomes negative. It is practically impossible to calculate analytically the ruin probability because the theoretical formula of the ruin probability contains the recursive convolutions and infinite sum. Hence, many authors have suggested approximation formulas of the ruin probability. We introduce a new approximation formula of the ruin probability which extends the well-known De Vylder's and exponential approximation formulas. We compare our approximation formula with the existing ones and show numerically that our approximation formula gives closer values to the true ruin probability in most cases.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.3
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• pp.180-193
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• 2023

Approximating the implied volatilities and estimating the model parameters are important topics in quantitative finance. This study proposes an approximation formula for short-maturity near-the-money implied volatilities in stochastic volatility models. A general second-order nonlinear PDE for implied volatility is derived in terms of time-to-maturity and log-moneyness from the Feyman-Kac formula. Using regularity conditions and the Taylor expansion, an approximation formula for implied volatility is obtained for short-maturity nearthe-money call options in two stochastic volatility models: Heston model and SABR model. In addition, we proposed a novel numerical method to estimate model parameters. This method reduces the number of model parameters that should be estimated. Generating sample data on log-moneyness, time-to-maturity, and implied volatility, we estimate the model parameters fitting the sample data in the above two models. Our method provides parameter estimates that are close to true values.

• ETRI Journal
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• v.15 no.3
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• pp.35-45
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• 1994

In this paper we develop an approximation formalism on the queue length distribution for general queueing models. Our formalism is based on two steps of approximation; the first step is to find a lower bound on the exact formula, and subsequently the Chernoff upper bound technique is applied to this lower bound. We demonstrate that for the M/M/1 model our formula is equivalent to the exact solution. For the D/M/1 queue, we find an extremely tight lower bound below the exact formula. On the other hand, our approach shows a tight upper bound on the exact distribution for both the ND/D/1 and M/D/1 queues. We also consider the $M+{\Sigma}N_jD/D/1$ queue and compare our formula with other formalisms for the $M+{\Sigma}N_jD/D/1$ and M+D/D/1 queues.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.4
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• pp.77-83
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• 1994

In this paper we numerically approximated the field-effect mobility of a-Si:H TFT. Field-effect mobility, based on the charge-trapping model and new effective capacitance model in our study, used Chebyshev approximation was approximated as the function of gate potential(gate-to-channel voltage). Even though various external factors are changed, this formula can be applied by choosing the characteristic coefficients without any change of the approximation formula corresponding to each operation region. Using new approximated field-effect mobility formula, the dependences of field-effect mobility on materials and thickness of gate insulator, thickness of a-Si bulk, and operation temperature in inverted staggered-electrode a-Si:H TFT were estimated. By this was the usefulness of new approximated mobility formula proved.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.43-52
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• 2002

By the use of Taylor's expansion formula with the integral remainder, an accurate approximation for the fiber refractive index profile is given.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.167-174
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• 2010

In this paper, we investigate the possibility of $2{\pi}$-periodic continuous function approximation by periodic neural networks. Using the Riemann sum and the quadrature formula, we show the capability of a periodic neural network approximation.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.173-185
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• 2014

In the present paper, we consider an anomalous diffusion problem in two dimensional space involving Caputo time and Riesz-Feller fractional derivatives and then solve it by using a series involving bilateral eigen-functions. Also, we obtain a numerical approximation formula of this problem and discuss some of its particular cases.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.16 no.28
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• pp.137-143
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• 1993

Generally there are three methods to derive an approximation formula: 1) approching standard normal distribution by appropriate changing variable 2) using standardization variable for expansion 3) deriving approximation formula by direct method. This paper present correction terms having the form of $C_{1/v^{n/2}}/{\;}+{\;}C_2{\;}(n=1,2)$ with respect to $x^2_{\alpha}(v)$ distribution (${\nu}{\;}{\leq}{\;}30$), which minimize the error by EDA method and least square method.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.641-648
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• 2007

In this paper, we present the exact Hausdorff distance between the offset curve of quadratic $B\'{e}zier$ curve and its quadratic $GC^1$ approximation. To illustrate the formula for the Hausdorff distance, we give an example of the quadratic $GC^1$ approximation of the offset curve of a quadratic $B\'{e}zier$ curve.