• Communications for Statistical Applications and Methods
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• 제25권2호
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• pp.217-234
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• 2018

Copulas are a tool for constructing multivariate distributions and formalizing the dependence structure between random variables. From copula literature review, there are a few asymmetric copulas available so far while data collected from the real world often exhibit asymmetric nature. This necessitates developing asymmetric copulas. In this study, we discuss a method to construct a new class of bivariate asymmetric copulas based on products of symmetric (sometimes asymmetric) copulas with powered arguments in order to determine if the proposed construction can offer an added value for modeling asymmetric bivariate data. With these newly constructed copulas, we investigate dependence properties and measure of association between random variables. In addition, the test of symmetry of data and the estimation of hyper-parameters by the maximum likelihood method are discussed. With two real example such as car rental data and economic indicators data, we perform the goodness-of-fit test of our proposed asymmetric copulas. For these data, some of the proposed models turned out to be successful whereas the existing copulas were mostly unsuccessful. The method of presented here can be useful in fields such as finance, climate and social science.

• Communications for Statistical Applications and Methods
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• 제30권5호
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• pp.467-483
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• 2023

In this research, a conversion function and a distortion associated with the conversion function are defined and used to derive a unit power Gompertz distortion. A new family of copulas is built using the global distorted function. Four base copulas, namely Clayton, Gumbel, Frank, and Gaussian, are distorted into the family. Some properties including tail dependence coefficients and tail order are examined. Kendall's tau formula is derived for new copulas when the base copula is Clayton, Gumbel, or Frank. The maximum pseudo-likelihood estimation method is employed, and a simulation study was performed. The log-likelihood and AIC are reported to compare the performance of the fitted copulas. According to the applied data, the results indicate that new distorted copulas with additional parameters improve the fit.

• 대한수학회보
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• 제54권3호
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• pp.839-874
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• 2017

Our goal is to establish and prove the almost sure central limit theorems for some order statistics $\{M_n^{(k)}\}$, $k=1,2,{\ldots}$, formed by stochastic processes ($X_1,X_2,{\ldots},X_n$), $n{\in}N$, the distributions of which are defined by certain Archimedean copulas. Some properties of generators of such the copulas are intensively used in our proofs. The first class of theorems stated and proved in the paper concerns sequences of ordinary maxima $\{M_n\}$, the second class of the presented results and proofs applies for sequences of the second largest maxima $\{M_n^{(2)}\}$ and the third (and the last) part of our investigations is devoted to the proofs of the almost sure central limit theorems for the k-th largest maxima $\{M_n^{(k)}\}$ in general. The assumptions imposed in the first two of the mentioned groups of claims significantly differ from the conditions used in the last - the most general - case.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2017년도 학술발표회
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• pp.421-421
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• 2017

현재 우리나라에서 끊임없이 발생하고 있는 폭풍해일로부터 연안지역의 안전을 확보하기 위해서는 태풍 시 파랑의 거동 및 특성을 정확히 예측하는 것이 중요하다. 폭풍해일 모의실험의 정확성을 향상시키고 폭풍해일의 위험성을 정량화하기 위해서는 해일파고, 파주기, 그리고 폭풍 지속시간 간의 상관성이 분석되어야한다. 이를 위해 본 연구에서는 Copulas(Archimedean) 이론을 이용하여 폭풍해일에 대한 다변량 통계분석이 이루어졌다. 동해안 연안에서 나타나는 파고, 파주기, 태풍 지속시간, 해면수위, 태풍 도착간격시간 간의 의존성을 켄달의 타우 상관계수를 이용하여 조사하였다. Copulas 다변량 통계분석의 결과, 오직 파고와 파주기, 그리고 태풍지속시간만이 명확한 상관성을 나타냈다.

• Communications for Statistical Applications and Methods
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• 제28권1호
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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.

• 한국수자원학회논문집
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• 제45권10호
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• pp.1043-1050
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• 2012

본 연구에서는 copulas 기반의 결합가뭄지수를 적용한 가뭄심도-영향면적-지속기간곡선을 작성하여 가뭄의 시공간적 거동을 살펴보았다. 우리나라 전국 60개 지점의 기상청 월강수량자료로부터 JDI를 산정한후, 이를 다시 EOF와 Kriging 기법을 이용하여 $10{\times}10$ km의 공간적 해상도를 가진 JDI 값으로 할당하였다. 격자기반의 JDIs를 가뭄의 지속기간별 영향면적별로 분석하고, 우리나라의 가뭄 사상을 표현하기 위하여 JDI-SAD 곡선을 작성하였다. JDI-SAD 곡선을 통하여 과거에 발생한 가뭄 사상을 시공간적으로 특성화할 수 있다. 또한 현재의 가뭄 상황에 대한 정확한 영향평가에 기여할 것으로 기대된다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권1호
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• pp.23-45
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• 2015

We consider counterparty risk in CDS rates. To do so, we use a multivariate jump diffusion process for obligors' default intensity, where jumps (i.e. magnitude of contribution of primary events to default intensities) occur simultaneously and their sizes are dependent. For these simultaneous jumps and their sizes, a homogeneous Poisson process. We apply copula-dependent default intensities of multivariate Cox process to derive the joint Laplace transform that provides us with joint survival/default probability and other relevant joint probabilities. For that purpose, the piecewise deterministic Markov process (PDMP) theory developed in [7] and the martingale methodology in [6] are used. We compute survival/default probability using three copulas, which are Farlie-Gumbel-Morgenstern (FGM), Gaussian and Student-t copulas, with exponential marginal distributions. We then apply the results to calculate CDS rates assuming deterministic rate of interest and recovery rate. We also conduct sensitivity analysis for the CDS rates by changing the relevant parameters and provide their figures.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권1호
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• pp.77-93
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• 2014

This paper focuses on computational contractual distinctions as an explanation for the spread between a forward contract and a similar futures contract which is derived and investigated. We evaluate this spread by constructing a time series model, which was established based on copula functions, and also show that the forward-futures spread is more significant for long maturity.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권3호
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• pp.299-313
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• 2015

In this paper, we show the effectiveness of copulas by comparing the correlation of market data of year 2010 with those of years 2006-2009 and investigate copula functions as pricing methods of digital and rainbow options through real market data. We propose an accurate method of pricing rainbow options by using the correlation coefficients obtained from the copula functions depending on strike prices between assetes instead of simple traditional correlation coefficients.

• 응용통계연구
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• 제30권2호
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• pp.203-213
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• 2017

우리는 이변량 경시적 자료의 조건부 결합 분포를 추정하기 위하여 회귀 모형과 코플라 모형을 연구하였다. 주변 분포의 추정을 위하여 시변 변환 모형을 고려하였고, 이변량 반응변수 각각에 대한 주변 분포를 가우시안 코플라를 이용하여 결합하여 조건부 결합 분포를 추정하였다. 우리가 제안한 모형은 조건부 평균 모형만으로 자료를 설명하기 어려운 경우에 적용될 수 있다. 시변 변환 모형과 가우시안 코플라 모형을 결합한 본 논문의 방법은 반복 측정된 이변량 경시적 자료에 대한 모형화가 용이하며 해석하기 쉬운 장점이 있다. 우리는 본 논문의 방법을 반복 측정된 이변량 콜레스테롤 자료를 분석하는데 적용하여 보았다.