• Communications for Statistical Applications and Methods
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• 제13권2호
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• pp.389-407
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• 2006

Extreme value theory has been used widely in many areas of science and engineering to deal with the assessment of extreme events which are rare but have catastrophic consequences. The potential of extreme value theory has only been recognized recently in finance area. In this paper, we provide an overview of extreme value theory for estimating and assessing value at risk and expected shortfall which are the methods for modelling and measuring the extreme financial risks. We illustrate that the approach based on extreme value theory is very useful for estimating tail related risk measures through backtesting of an empirical data.

• 응용통계연구
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• 제20권2호
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• pp.291-311
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• 2007

전 세계적으로 금융시장에서는 예측할 수 없는 대형 사건들이 지속적으로 일어나고 있으며, 특히 보험시장의 경우에는 대재해성(catastrophe)손실 등을 포함한 극단적 사건에 대한 예측이 날이 갈수록 어려워지고 있는바 극단적 위험관리에 대한 필요성이 증대되고 있다. 극단적 위험관리에 있어 분포의 꼬리영역만을 분리하여 그 정보를 최대로 이용하는 방법이 필요한데, 이러한 문제들을 해결하기 위해 극단치들의 움직임을 모형화 하는 소위 극단치 이론(Extreme Value Theory: EVT)을 이용하는 것이 요구된다. 극단치 이론은 현재 여러 분야에서 활용되고 있는데, 특히 금융시장에서는 극단적 변화가 미치는 영향을 분석하기 위해서 극단치 이론을 이용한 금융위험분석을 실시하고 있다. 본 연구에서는 위험관리에 있어서 극단치 이론의 중요성을 검토하고 보험사의 위험자본에 초점을 맞추어 손실 발생의 극단적 위험을 측정하고 이에 대비한 위험자본의 적정규모를 측정하여 보았다.

• 한국산업융합학회 논문집
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• 제8권2호
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• pp.85-95
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• 2005

The margin level in the futures market platys an important role in balancing the default probability with the investor's opportunity cost. In this paper, we investigate whether the movement of KOSPI200 futures daily prices can be modeled with the extreme value theory. Based on this investigation, we examine the validity of the margin level set by the extreme value theory. Moreover, we propose an expected profit-maximization model for securities companies. In this model, the extreme value theory is used for cost estimation, and a regression analysis is used for revenue calculation. Computational results are presented to compare the extreme value distribution with the empirical distribution of margin violation in KOSPI200 and to examine the suitability of the expected profit-maximization model.

• 대한산업공학회지
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• 제33권4호
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• pp.410-418
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• 2007

This article suggests the methods to investigate adverse movement across global stock markets arising from insolvency of subprime mortgage in U.S. Our application deals with asymptotic tail dependence of daily stock index returns (KOSPI, DJIA, Shanghai Composite) of three countries; Korea, U.S., and China, over specific period via extreme value theory and copula functions. Daily stock index returns among three countries show higher extremal dependence during the period exposed to systematic shock. We confirm that extreme value theory and copula functions have potential to well describe the extreme dependence between three countries' daily stock index returns.

• Wind and Structures
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• 제31권3호
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• pp.197-207
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• 2020

Knowledge on the design value of extreme wind pressure coefficients (EWPC) of a specific zone of buildings is essential for the wind-resistant capacity of claddings. This paper presents a method to estimate the representative EWPC introducing the multivariate extreme value model. The spatial correlations of the extreme wind pressures at different locations can be consider through the multivariate extreme value. The moving average method is also adopted in this method, so that the measured point pressure can be converted to wind pressure of an area. The proposed method is applied to wind tunnel test results of a large flat roof building. Comparison with existing methods shows that it can give a good estimation for all target zones with different sizes.

• 응용통계연구
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• 제19권3호
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• pp.481-504
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• 2006

금융위험의 측정 및 관리를 위한 도구로서 분포의 꼬리 부분과 관련한 위험척도로 VaR가 현재 널리 활용되고 있다. 특히 VaR의 정확한 추정을 위해 정규분포를 가정한 기존의 방법보다는 극단치이론을 이용한 방법이 최근 관심을 끌고 있다. 지금까지 극단치이론을 이용한VaR의 추정에 관한 연구는 대부분 단변량의 경우에 대해 이루어졌다. 본 논문에서는 코퓰러를 극단치이론에 결부시켜 다변량 극단치분포를 모형화하여 포트폴리오 위험측정을 다루고 있다. 특히 본 연구에서는 포트폴리오 위험 척도로 VaR와 더불어 ES에 대한 추정 방법도 함께 논의하였다. 포트폴리오 위험측정을 위한 방법으로 본 논문에서 논의한 코퓰러-극단치이론에 의한 접근방법이 기존의 분산-공분산 방법보다 상대적으로 우수한지를 실증자료에 대한 사후검증을 통해 살펴보았다.

• Nuclear Engineering and Technology
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• 제47권1호
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• pp.59-65
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• 2015

Background: After the Fukushima accident, the importance of hazard analysis for extreme external events was raised. Methods: To analyze typhoon-induced hazards, which are one of the significant disasters of East Asian countries, a statistical analysis using the extreme value theory, which is a method for estimating the annual exceedance frequency of a rare event, was conducted for an estimation of the occurrence intervals or hazard levels. For the four meteorological variables, maximum wind speed, instantaneous wind speed, hourly precipitation, and daily precipitation, the parameters of the predictive extreme value theory models were estimated. Results: The 100-year return levels for each variable were predicted using the developed models and compared with previously reported values. It was also found that there exist significant long-term climate changes of wind speed and precipitation. Conclusion: A fragility analysis should be conducted to ensure the safety levels of a nuclear power plant for high levels of wind speed and precipitation, which exceed the results of a previous analysis.

• 한국해양공학회지
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• 제33권3호
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• pp.222-228
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• 2019

An extreme value analysis (EVA) is essential to obtain a design value for highly nonlinear variables such as long-term environmental data for wind and waves, and slamming or sloshing impact pressures. According to the extreme value theory (EVT), the extreme value distribution is derived by multiplying the initial cumulative distribution functions for independent and identically distributed (IID) random variables. However, in the position mooring of DNVGL, the sampled global maxima of the mooring line tension are assumed to be IID stochastic variables without checking their independence. The ITTC Recommended Procedures and Guidelines for Sloshing Model Tests never deal with the independence of the sampling data. Hence, a design value estimated without the IID check would be under- or over-estimated because of considering observations far away from a Weibull or generalized Pareto distribution (GPD) as outliers. In this study, the IID sampling data are first checked in an EVA. With no IID random variables, an automatic resampling scheme is recommended using the block maxima approach for a generalized extreme value (GEV) distribution and peaks-over-threshold (POT) approach for a GPD. A partial autocorrelation function (PACF) is used to check the IID variables. In this study, only one 5 h sample of sloshing test results was used for a feasibility study of the resampling IID variables approach. Based on this study, the resampling IID variables may reduce the number of outliers, and the statistically more appropriate design value could be achieved with independent samples.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2004년도 춘계공동학술대회 논문집
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• pp.734-737
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• 2004

When the margin level is set relatively low, margin violation probability increases and the default probability of the futures market rises. On the other hand, if the margin level is set high, the margin violation probability decreases, but the futures market becomes less attractive to hedgers as the investor's opportunity cost increases. In this paper, we investigate whether the movement of KOSPI200(Korea Composite Stock Price Index 200) futures daily prices can be modeled with the extreme value theory. Base on this investigation, we examine the validity of the margin level set by the extreme value theory. Computational results are presented to compare the extreme value distribution and the empirical distribution of margin violation in KOSPI200. Some observations and implications drawn from the computational experiment are also discussed.

• 응용통계연구
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• 제23권2호
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• pp.219-234
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• 2010

시가총액에 따른 인덱스(INDEX) 투자를 했을 경우에, VaR(Value at Risk)을 종합주가지수(KOSPI)로부터 얻은 수익율의 극단 손실값들로부터 추정한다. 이를 위해, 극단값 이론 중 BM(Block Maxima) 모형을 적용하며, 극단 손실값들의 비독립적 발생을 고려하기 위하여, extremal index 역시 추정한다. 모형의 타당성을 알아보기 위해, 실패율방법을 이용한 사후검정 (back-testing) 을 실시한다. 사후검정을 통해, BM 모형을 적용한 VaR의 추정이 적절함을 알 수 있었다. 또한, 일반적으로 많이 사용되는 GARCH 모형을 이용한 VaR의 추정과 비교한다. 이를 통해, 오차가 t-분포를 따른다고 가정하는 경우, GARCH 모형을 이용한 VaR의 추정이 BM 모형을 이용한 경우와 사후 검정결과에 차이가 없음을 확인하였다. 그러나, GARCH 모형을 통한 VaR 추정은 추정시점근방의 극단 손실값들에 민감하게 반응하지만, BM 모형은 그렇지 않았다. 따라서, 현 시점으로부터 단기간동안의 손실위험은 GARCH 모형을 이용한 VaR의 추정값을 사용하는 것이 적절하며, 장기간동안의 손실위험은 BM 모형으로부터 얻은 VaR의 추정값을 사용하는 것이 적절하다.