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Search Results: 1 - 10 of 36 matches for " copulas "
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Modeling and Quantifying of the Global Wrong Way Risk  [PDF]
Badreddine Slime
Journal of Financial Risk Management (JFRM) , 2017, DOI: 10.4236/jfrm.2017.63017
Abstract: The counterparty risk issue has become increasingly important in the world of finance. This risk is defined as the loss due to the counterparty default. The regulator uses the Credit Value Adjustment (CVA) to measure this risk. However, there is the independency assumption between the default and the exposure behind the CVA computation and it is not verified on the financial market. This paper presents two mathematical models for the assessment and the quantification of the counterparty risk without this assumption. This kind of risk is known as Wrong Way Risk (WWR). This study focuses on three approaches: empirical, copula and mixed model. The first one is based on the hazard rate modelling to express the correlation between the probability of default and the exposure. The second one is about calculating the WWR effect using copulas. The last one is a combination of both. There is another assumption that makes easier the CVA computation: The constant of the loss given default (LGD). As we know this assumption is not verified because the LGD could be deterministic or stochastic. Otherwise, it could lead to a
The distribution of ser and estar with adjectives: A critical survey
Revista signos , 2011, DOI: 10.4067/S0718-09342011000100004
Abstract: explaining the distribution of the two spanish copulas, ser and estar, is still a challenge in current linguistic theory. the aim of the present paper is to provide a critical synthesis and comparison of some of the most influential theoretical proposals that have been put forward to account for the complex distribution of ser and estar with adjectives. first, a general description of the distribution and interpretation of the two spanish copulas is provided. then, after showing the inadequacy of the traditional account that views ser and estar as the permanent and temporal copulas respectively, the different semantic, aspectual, semantic-syntactic and pragmatic approaches to explaining their distribution are reviewed. it is observed that most of the recent analyses converge on the following: (i) ser is more flexible than estar in temporal terms, and (ii) ser is independent from the discursive context while estar is always linked to discourse.
应用概率统计 , 2014,
Abstract: 本文研究了配备Farlie-Gumbel-MorgensternCopulas的二维随机向量之和的相依性,得到了在这类Copulas函数下两个独立的随机向量之和的Kendall及Spearman相依系数的一般公式;并针对边缘分布分别为指数分布的情况推导出了具体的公式;证明了当边缘分布满足一定的条件时,不存在尾部相依性.此外,对于几种不同边缘分布的情况进行了随机模拟与比较.这些方法及结果对两个企业(公司)合并后某两个随机指标之间的相依性问题的研究具有理论指导意义,为这类问题的进一步探索提供了理论基础.
Risk Aggregation by Using Copulas in Internal Models  [PDF]
Tristan Nguyen, Robert Danilo Molinari
Journal of Mathematical Finance (JMF) , 2011, DOI: 10.4236/jmf.2011.13007
Abstract: According to the Solvency II directive the Solvency Capital Requirement (SCR) corresponds to the economic capital needed to limit the probability of ruin to 0.5%. This implies that (re-)insurance undertakings will have to identify their overall loss distributions. The standard approach of the mentioned Solvency II directive proposes the use of a correlation matrix for the aggregation of the single so-called risk modules respectively sub-modules. In our paper we will analyze the method of risk aggregation via the proposed application of correlations. We will find serious weaknesses, particularly concerning the recognition of extreme events, e. g. natural disasters, terrorist attacks etc. Even though the concept of copulas is not explicitly mentioned in the directive, there is still a possibility of applying it. It is clear that modeling dependencies with copulas would incur significant costs for smaller companies that might outbalance the resulting more precise picture of the risk situation of the insurer. However, incentives for those companies who use copulas, e. g. reduced solvency capital requirements compared to those who do not use it, could push the deployment of copulas in risk modeling in general.
Estimation of Distribution Algorithm with Multivariate T-Copulas for Multi-Objective Optimization  [PDF]
Ying Gao, Lingxi Peng, Fufang Li, Miao Liu, Xiao Hu
Intelligent Control and Automation (ICA) , 2013, DOI: 10.4236/ica.2013.41009

Estimation of distribution algorithms are a class of evolutionary optimization algorithms based on probability distribution model. In this article, a Pareto-based multi-objective estimation of distribution algorithm with multivariate T-copulas is proposed. The algorithm employs Pareto-based approach and multivariate T-copulas to construct probability distribution model. To estimate joint distribution of the selected solutions, the correlation matrix of T-copula is firstly estimated by estimating Kendall’s tau and using the relationship of Kendall’s tau and correlation matrix. After the correlation matrix is estimated, the degree of freedom of T-copula is estimated by using the maximum likelihood method. Afterwards, the Monte Carte simulation is used to generate new individuals. An archive with maximum capacity is used to maintain the non-dominated solutions. The Pareto optimal solutions are selected from the archive on the basis of the diversity of the solutions, and the crowding-distance measure is used for the diversity measurement. The archive gets updated with the inclusion of the non-dominated solutions from the combined population and current archive, and the archive which exceeds the maximum capacity is cut using the diversity consideration. The proposed algorithm is applied to some well-known benchmark. The relative experimental results show that the algorithm has better performance and is effective.

On approximation of copulas
Tomasz Kulpa
International Journal of Mathematics and Mathematical Sciences , 1999, DOI: 10.1155/s0161171299222594
Abstract: New sufficient conditions for strong approximation of copulas, generated by sequences of partitions of unity, are given. Results are applied to the checkerboard and Bernstein approximations.
Global Risk Evolution and Diversification: a Copula-DCC-GARCH Model Approach
Marcelo Brutti Righi,Paulo Sergio Ceretta
Revista Brasileira de Finan?as , 2012,
Abstract: In this paper we estimate a dynamic portfolio composed by the U.S., German, British, Brazilian, Hong Kong and Australian markets, the period considered started on September 2001 and finished in September 2011. We ran the Copula-DCC-GARCH model on the daily returns conditional covariance matrix. The results allow us to conclude that there were changes in portfolio composition, occasioned by modifications in volatility and dependence between markets. The dynamic approach significantly reduced the portfolio risk if compared to the traditional static approach, especially in turbulent periods. Furthermore, we verified that the estimated copula model outperformed the conventional DCC model for the sample studied.
Analysis of Crude Oil and Gasoline Prices through Copulas
Ricardo de Melo e Silva Accioly,Fernando Antonio Lucena Aiube
Cadernos do IME : Série Estatística , 2008,
Abstract: In this paper we investigate the dependence of crude oil and gasoline prices. The understanding of the behavior of this dependence is useful for modeling the portfolio of investments in an integrated oil company. An accurate simulation of the behavior of these prices reveals precisely the risk and return of the portfolio. Morover the movements of these prices is crucial for goverment planing since they affect the overall economy of developed and developing countries. The classical approach which uses elliptical distributions to model the risk factors can be misleading since they are actually not elliptical. We used copula to establicsh such dependence since this methodolgy precludes the use of elliptical distributions. We found a change in the behavior of prices in the recent period compared to those in beginning of the decade and this fact is also reported in the literature. This change is observed through different copula models that were adjusted. These results were confirmed with a bootstrap analysis.
Nonlinear Principal and Canonical Directions from Continuous Extensions of Multidimensional Scaling  [PDF]
Carles M. Cuadras
Open Journal of Statistics (OJS) , 2014, DOI: 10.4236/ojs.2014.42015

A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.

暨南大学学报(自然科学与医学版) , 2013,
Abstract: 给出了已知水平(垂直)截面为有理函数截面的copula构造方法,并确定了对称copula、Archimedeancopula函数,证明了水平(垂直)截面为二次有理函数的Archimedeancopula函数的不存在性.
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