• The Korean Journal of Applied Statistics
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• v.30 no.2
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• pp.243-257
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• 2017

In this paper, we compare several methods to approximate option prices: Edgeworth expansion, A-type and C-type Gram-Charlier expansions, a method using normal inverse gaussian (NIG) distribution, and an asymptotic method using nonlinear regression. We used two different types of approximation. The first (called the RNM method) approximates the risk neutral probability density function of the log return of the underlying asset and computes the option price. The second (called the OPTIM method) finds the approximate option pricing formula and then estimates parameters to compute the option price. For simulation experiments, we generated underlying asset data from the Heston model and NIG model, a well-known stochastic volatility model and a well-known Levy model, respectively. We also applied the above approximating methods to the KOSPI200 call option price as a real data application. We then found that the OPTIM method shows better performance on average than the RNM method. Among the OPTIM, A-type Gram-Charlier expansion and the asymptotic method that uses nonlinear regression showed relatively better performance; in addition, among RNM, the method of using NIG distribution was relatively better than others.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.5C
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• pp.413-421
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• 2008

The paper derives asymptotic formulas for the MSE distortion and the signal-to-noise ratio of a mismatched fixed-rate minimum MSE Laplacian quantizer. These closed-form formulas are expressed in terms of the number N of quantization points, the mean displacement $\mu$, and the ratio $\rho$ of the standard deviation of the source to that for which the quantizer is optimally designed. Numerical results show that the principal formula is accurate in that, for rate R=$log_2N{\geq}6$, it predicts signal-to-noise ratios within 1% of the true values for a wide range of $\mu$, and $\rho$. The new findings herein include the fact that, for heavy variance mismatch of ${\rho}>3/2$, the signal-to-noise ratio increases at the rate of $9/\rho$ dB/bit, which is slower than the usual 6 dB/bit, and the fact that an optimal uniform quantizer, though optimally designed, is slightly more than critically mismatched to the source. It is also found that signal-to-noise ratio loss due to $\mu$ is moderate. The derived formulas can be useful in quantization of speech or music signals, which are modeled well as Laplacian sources and have changing short-term variances.

• The Korean Journal of Ecology
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• v.27 no.1
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• pp.27-33
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• 2004

Cryptomeria japonica plantation was monitored every year during 15 years from 1983 to 1997 for stem diameter and volume. The reciprocal equation, 1/Y = A + B/N, was applied to the relationship between cumulative volume Y and cumulative number N from the largest tree in the stand each year. The parameters A and B, which means respectively the reciprocal of an asymptotic value of total stand stem volume and the reciprocal of the maximum stem volume, are related by a power function. The power functional relationship between A and B derived a linear relationship of B-points ( $N_{B}$, $V_{B}$; $N_{B}$ = B/A, $Y_{B}$ = 1/2A) of each Y-N curve on log-log coordinates. The gradient of B-point line was so steep that the Y-N curve moved parallel upward year by year. The time trajectory of mean stem volume (W) and density ($\rho$) provided evidence in favor of the 3/2 power law of self-thinning, because the gradient of W - $\rho$ trajectory on log-log coordinates approximated to -3/2 at the final stage of stand development. On the basis of the results of Y-N curves and W - $\rho$ trajectory, the time trajectory of maximum stem volume $W_{max obs}$ and $\rho$ was derived theoretically. The gradient of $W_{max obs}$ - $\rho$ trajectory on log-log coordinates is calculated to be -0.6105 at the final stage. The gradient of $W_{max obs}$ - $\rho$ trajectory was steeper than that of W - $\rho$ trajectory at the early stage, while the former is gentler than the latter at the later stage.stage.e.age.e.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.39 no.2
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• pp.143-156
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• 2015

The stress and displacement fields at the crack tip were studied during the unsteady propagation of a mode III crack in a direction that was different from the property graduation direction in functionally graded materials (FGMs). The property graduation in FGMs was assumed based on the linearly varying shear modulus under a constant density and the exponentially varying shear modulus and density. To obtain the solution of the harmonic function, the general partial differential equation of the dynamic equilibrium equation was transformed into a Laplace equation. Based on the Laplace equation, the stress and displacement fields, which depended on the time rates of change in the crack tip speed and stress intensity factor, were obtained through an asymptotic analysis. Using the stress and displacement fields, the effects of the angled property variation on the stresses, displacements, and stress intensity factors are discussed.

• The KSFM Journal of Fluid Machinery
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• v.15 no.3
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• pp.12-18
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• 2012

The Lattice Boltzmann Method has developed for solving the Boltzmann equation in Cartesian domains containing immersed boundaries of arbitrary geometrical complexity moving with prescribed kinematics. When a immersed boundaries are sweeping the fixed fluid node, refilling the node information in a vicinity of fluid nodes is one of the important issues in Lattice Boltzmann Method. In this study, we propose a simple refill algorithm for the particle distribution function based on a proper velocity, density and strain rate to enhance accuracy and stability of the method. The refill scheme based on a asymptotic analysis of LBGK model has improved accuracy than interpolation schemes. The proposed scheme in this study is validated by the simulations of an impulsively started rotating circular cylinder to investigate adaptability for fluid-structure interaction (FSI) problem. This refill scheme has improved stability and accuracy especially at high Reynolds number region.

• Journal of the Korean Statistical Society
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• v.30 no.2
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• pp.179-192
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• 2001

When a statistical model has a hierarchical structure such as multilayer perceptrons in neural networks or Gaussian mixture density representation, the model includes distribution with unidentifiable parameters when the structure becomes redundant. Since the exact structure is unknown, we need to carry out statistical estimation or learning of parameters in such a model. From the geometrical point of view, distributions specified by unidentifiable parameters become a singular point in the parameter space. The problem has been remarked in many statistical models, and strange behaviors of the likelihood ratio statistics, when the null hypothesis is at a singular point, have been analyzed so far. The present paper studies asymptotic behaviors of the maximum likelihood estimator and the Bayesian predictive estimator, by using a simple cone model, and show that they are completely different from regular statistical models where the Cramer-Rao paradigm holds. At singularities, the Fisher information metric degenerates, implying that the cramer-Rao paradigm does no more hold, and that he classical model selection theory such as AIC and MDL cannot be applied. This paper is a first step to establish a new theory for analyzing the accuracy of estimation or learning at around singularities.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.7
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• pp.851-858
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• 2010

A generalized elastic solution for a transient mode III crack propagating along the gradient in functionally graded materials (FGMs) is obtained through an asymptotic analysis. The shear modulus and density of the FGMs are assumed to vary exponentially along the gradient. The stress and displacement fields near the crack tip are obtained in terms of powers of radial coordinates, and the coefficients depend on the time rates of the change of the crack tip speed and stress intensity factors. The influence of nonhomogeneity and transients on the higher order terms of the stress and displacement fields is discussed.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.429-437
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• 2013

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be independent and identically distributed random variables having common exponential density with unknown mean ${\mu}$. In the sequential confidence interval estimation for the exponential hazard rate ${\theta}=1/{\mu}$, when the loss function is strictly convex, the following stopping rule is proposed with the half length d of prescribed confidence interval $I_n$ for the parameter ${\theta}$; ${\tau}$ = smallest integer n such that $n{\geq}z^2_{{\alpha}/2}\hat{\theta}^2/d^2+2$, where $\hat{\theta}=(n-1)\bar{X}{_n}^{-1}/n$ is the minimum risk estimator for ${\theta}$ and $z_{{\alpha}/2}$ is defined by $P({\mid}Z{\mid}{\leq}{\alpha}/2)=1-{\alpha}({\alpha}{\in}(0,1))$ Z ~ N(0, 1). For the confidence intervals $I_n$ which is required to satisfy $P({\theta}{\in}I_n){\geq}1-{\alpha}$. These estimated intervals $I_{\tau}$ have the asymptotic consistency of the sequential procedure; $$\lim_{d{\rightarrow}0}P({\theta}{\in}I_{\tau})=1-{\alpha}$$, where ${\alpha}{\in}(0,1)$ is given.

• 전기의세계
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• v.44 no.3
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• pp.9-14
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• 1995

비정질 core의 Butt-lap-step joint model의 자계를 유한요소법을 이용하여 해석한 결과, step당 리본 수의 변화, 설계자속밀도의 변화, 코아 연결부의 형상 변화에 따른 특성을 분석하면 다음과 같이 요약할 수 있다. (1) Step당 리본 수의 변화에 따른 영향에서 리본수가 작을수록 코아 전체의 flux density의 편차가 작으며 최대값 역시 낮으므로 유리하다. (2) 설계자속밀도의 변화에 따른 코아 부위의 자속 변화는 인가하는 설계자속밀도의 값이 높을수록 균일한 자장 분포를 얻을 수 있다. (3) 코아의 적층 방법의 변화에서는 Butt-Lap-Step방식이 가장 유리한 결과를 얻을 수 있었지만 코아 곡률부의 형상 변화가 중요한 요소로 작용한다. (4) 최적 step수, ribbon/group 수, airgap 길이 등은 전체 model의 특성, 손실, 제작성 등을 고려하여 결정하는 것이 바람직하며, 유한요소법의 해석으로는 전체적인 비정질 코아 변압기의 전기적인 특성과 경향을 도식화하여 설계자에게 좋은 설계방향과 정보를 제공할 수 있게 된다. 또한 비정질 코아의 특성상 종래의 일반적인 유한요소법으로는 많은 계산시간과 큰 computer system을 요구하는 core의 미세부분의 해석은 새로운 계산기법을 도입하여 계산해야 할 것이다. 이러한 문제해결을 위하여 3절에서 설명한 Asymptotic Expansion을 이용하여 균질화(homogenized)된 투자율 (또는 reluctivity)를 산출하고, 여기에 유한요소기법을 도입하여 단점을 보완한 새로운 기법의 algorithm을 개발하고 있으며, 이 기법은 계산시간의 단축과 Microscopic하게 자속밀도 분포를 관찰 할 수 있으므로 joint 부분의 자속경로와 손실 등 비정질 코아의 설계 Parameter를 설정하는 결정적인 역할을 할수 있을 것으로 기대된다.

• Journal of Korea Water Resources Association
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• v.39 no.12 s.173
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• pp.997-1012
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• 2006

We have presented a nonparametric stochastic approach for the SOI(Southern Oscillation Index) series that used nonlinear methodology called Nonlinear AutoRegressive(NAR) based on conditional kernel density function and CAFPE(Corrected Asymptotic Final Prediction Error) lag selection. The fitted linear AR model represents heteroscedasticity, and besides, a BDS(Brock - Dechert - Sheinkman) statistics is rejected. Hence, we applied NAR model to the SOI series. We can identify the lags 1, 2 and 4 are appropriate one, and estimated conditional mean function. There is no autocorrelation of residuals in the Portmanteau Test. However, the null hypothesis of normality and no heteroscedasticity is rejected in the Jarque-Bera Test and ARCH-LM Test, respectively. Moreover, the lag selection for conditional standard deviation function with CAFPE provides lags 3, 8 and 9. As the results of conditional standard deviation analysis, all I.I.D assumptions of the residuals are accepted. Particularly, the BDS statistics is accepted at the 95% and 99% significance level. Finally, we split the SOI set into a sample for estimating themodel and a sample for out-of-sample prediction, that is, we conduct the one-step ahead forecasts for the last 97 values (15%). The NAR model shows a MSEP of 0.5464 that is 7% lower than those of the linear model. Hence, the relevance of the NAR model may be proved in these results, and the nonparametric NAR model is encouraging rather than a linear one to reflect the nonlinearity of SOI series.