• Title/Summary/Keyword: Approximation formula

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A New Approach for the Derivation of a Discrete Approximation Formula on Uniform Grid for Harmonic Functions

  • Kim, Philsu;Choi, Hyun Jung;Ahn, Soyoung
    • 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 ${\nabla}^2$.

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An Improvement of the Approximation of the Ruin Probability in a Risk Process (보험 상품 파산 확률 근사 방법의 개선 연구)

  • Lee, Hye-Sun;Choi, Seung-Kyoung;Lee, Eui-Yong
    • 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.

APPROXIMATION FORMULAS FOR SHORT-MATURITY NEAR-THE-MONEY IMPLIED VOLATILITIES IN THE HESTON AND SABR MODELS

  • HYUNMOOK CHOI;HYUNGBIN PARK;HOSUNG RYU
    • 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.

APPROXIMATION OF THE QUEUE LENGTH DISTRIBUTION OF GENERAL QUEUES

  • Lee, Kyu-Seok;Park, Hong-Shik
    • 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.

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Chebyshev Approximation of Field-Effect Mobility in a-Si:H TFT (비정질 실리콘 박막 트랜지스터에서 전계효과 이동도의 Chebyshev 근사)

  • 박재홍;김철주
    • 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.

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THE CAPABILITY OF PERIODIC NEURAL NETWORK APPROXIMATION

  • Hahm, Nahmwoo;Hong, Bum Il
    • 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.

A GENERAL SOLUTION OF A SPACE-TIME FRACTIONAL ANOMALOUS DIFFUSION PROBLEM USING THE SERIES OF BILATERAL EIGEN-FUNCTIONS

  • Kumar, Hemant;Pathan, Mahmood Ahmad;Srivastava, Harish
    • 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.

Improving Percentile Points of $x^2$ Distribution ($x^2$분포의 백분위수의 개선에 관한 연구)

  • 이희춘
    • 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.

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HAUSDORFF DISTANCE BETWEEN THE OFFSET CURVE OF QUADRATIC BEZIER CURVE AND ITS QUADRATIC APPROXIMATION

  • Ahn, Young-Joon
    • 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.