• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.59-79
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• 2021

Value at Risk (VaR) is one of the most common risk management tools in finance. Since a portfolio of several assets, rather than one asset portfolio, is advantageous in the risk diversification for investment, VaR for a portfolio of two or more assets is often used. In such cases, multivariate distributions of asset returns are considered to calculate VaR of the corresponding portfolio. Copulas are one way of generating a multivariate distribution by identifying the dependence structure of asset returns while allowing many different marginal distributions. However, they are used mainly for bivariate distributions and are not widely used in modeling joint distributions for many variables in finance. In this study, we would like to examine the performance of various copulas for high dimensional data and several different dependence structures. This paper compares copulas such as elliptical, vine, and hierarchical copulas in computing the VaR of portfolios to find appropriate copula functions in various dependence structures among asset return distributions. In the simulation studies under various dependence structures and real data analysis, the hierarchical Clayton copula shows the best performance in the VaR calculation using four assets. For marginal distributions of single asset returns, normal inverse Gaussian distribution was used to model asset return distributions, which are generally high-peaked and heavy-tailed.

• The Korean Journal of Financial Management
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• v.26 no.3
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• pp.139-169
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• 2009

This paper introduces the modified VaR which takes into account the asymmetry and fat-tails of financial asset distribution, and then compares its out-of-sample forecast performance with traditional VaR model such as historical simulation model and Riskmetrics. The empirical tests using stock indices of 6 countries showed that the modified VaR has the best forecast accuracy. At the test of independence, Riskmetrics and GARCH model showed best performances, but the independence was not rejected for the modified VaR. The Monte Carlo simulation using skew t distribution again proved the best forecast performance of the modified VaR. One of many advantages of the modified VaR is that it is appropriate for measuring VaR of the portfolio, because it can reflect not only the linear relationship but also the nonlinear relationship between individual assets of the portfolio through coskewness and cokurtosis. The empirical analysis about decomposing VaR of the portfolio of 6 stock indices confirmed that the component VaR is very useful for the re-allocation of component assets to achieve higher Sharpe ratio and the active risk management.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.753-771
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• 2016

Value at Risk (VaR) is widely used as an important tool for risk management of financial institutions. In this paper we discuss estimation and back testing for VaR of the portfolio composed of KOSPI, Dow Jones, Shanghai, Nikkei indexes. The copula functions are adopted to construct the multivariate distributions of portfolio components from marginal distributions that combine extreme value theory and GARCH models. Volatility models with t distribution of the error terms using Gaussian, t, Clayton and Frank copula functions are shown to be more appropriate than the other models, in particular the model using the Frank copula is shown to be the best.

• Restorative Dentistry and Endodontics
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• v.27 no.2
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• pp.158-174
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• 2002

The aim of this study was to investigate the effect of light irradiation modes on polymerization shrinkage, degree of cure and microleakage of a composite resin. VIP$^{TM}$ (Bisco Dental Products, Schaumburg, IL, USA) and Optilux 501$^{TM}$ (Demetron/Kerr, Danbury, CT, USA) were used for curing Filtek$^{TM}$ Z-250 (3M Dental Products, St. Paul., MN, USA) composite resin using following irradiation modes: VIP$^{TM}$ (Bisco) 200mW/$\textrm{cm}^2$ (V2), 400mW/$\textrm{cm}^2$ (V4), 600mW/$\textrm{cm}^2$ (V6), Pulse-delay (200 mW/$\textrm{cm}^2$ 3 seconds, 5 minutes wait, 600mW/$\textrm{cm}^2$ 30seconds, VPD) and Optilux 501$^{TM}$ (Demetron/Kerr) C-mode (OC), R-mode (OR). Linear polymerization shrinkage of the composite specimens were measured using Linometer (R&B, Daejeon, Korea) for 90 seconds for V2, V4, V6, OC, OR groups and for up to 363 seconds for VPD group (n=10, each). Degree of conversion was measured using FTIR spectrometer (IFS 120 HR, Bruker Karlsruhe, Germany) at the bottom surface of 2 mm thick composite specimens V2, Y4, V6, OC groups were measured separately at five irradiation times (5, 10, 20, 40, 60 seconds) and OR, VPD groups were measured in the above mentioned irradiation modes (n=5 each). Microhardness was measured using Digital microhardness tester (FM7, Future-Tech Co., Tokyo, Japan) at the top and bottom surfaces of 2mm thick composite specimens after exposure to the same irradiation modes as the test of degree of conversion(n=3, each). For the microleakage test, class V cavities were prepared on the distal surface of the ninety extracted human third molars. The cavities were restored with one of the following irradiation modes : V2/60 seconds, V4/40 seconds, V6/30 seconds, VPD , OC and OR. Microleakage was assessed by dye penetration along enamel and dentin margins of cavities. Mean polymerization shrinkage, mean degree of conversion and mean microhardness values for all groups at each time were analyzed using one-way ANOVA and Duncan's multiple range test, and using chi-square test far microleakage values. The results were as follows : . Polymerization shrinkage was increased with higher light intensity in groups using VIP$^{TM}$ (Bisco) : the highest with 600mW/$\textrm{cm}^2$, followed by Pulse-delay, 400mW/$\textrm{cm}^2$ and 200mW/$\textrm{cm}^2$ groups, The degree of polymerization shrinkage was higher with Continuous mode than with Ramp mode in groups using Optilux 501$^{TM}$ (Demetron/Kerr). . Degree of conversion and microhardness values were higher with higher light intensity. The final degree of conversion was in the range of 44.7 to 54.98% and the final microhardness value in the range of 34.10 to 56.30. . Microleakage was greater in dentin margin than in enamel margin. Higher light intensity showed more microleakage in dentin margin in groups using VIP$^{TM}$ (Bisco). The microleakage was the lowest with Continuous mode in enamel margin and with Ramp mode in dentin margin when Optilux 501$^{TM}$ (Demetron/Kerr) was used.