Estimation of Distribution Algorithms (EDAs) are implemented mainly by the three steps: selecting the promising subset from the current population, modeling the distribution of the selected population and sampling from the estimated model. Modeling and sampling are key steps of EDAs. They are also research topic of copula theory to represent the multivariate joint distribution by a copula and t...

1. Abstract For the performance measure approach (PMA) of RBDO, a transformation between the input random variables and the standard normal random variables is required to carry out the inverse reliability analysis. Since the transformation uses the joint cumulative density function (CDF) of input variables, the joint CDF should be known before carrying out RBDO. In many industrial RBDO problem...

copula functions are powerful tools that describe dependence structure of multi- dimension random variables and are considered as one of the newest tools for risk management. one application of copula functions in risk management is calculating value at risk that can assert is the most widely used risk measures in financial institutions. in this article which primary goal is estimating more acc...

The tail behavior of sums of dependent risks was considered by Wüthrich (2003) and by Alink et al. (2004, 2005) in the case where the variables are exchangeable and connected through an Archimedean copula model. It is shown here how their result can be extended to a broader class of dependence structures using multivariate extreme-value theory. An explicit form is given for the asymptotic proba...

Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with the Gaussian copula hypothesis, while this hypothesis can be rejected for th...

This paper concentrates on estimating the risk of Title Transfer Facility (TTF) Hub natural gas portfolios by using the GARCH-EVT-copula model. We first use the univariate ARMA-GARCH model to model each natural gas return series. Second, the extreme value distribution (EVT) is fitted to the tails of the residuals to model marginal residual distributions. Third, multivariate Gaussian copula and ...

Empirical copula is a non-parametric algorithm to estimate the dependence structure of highdimensional arbitrarily distributed data. The computation of empirical copula is, however, very costly so that it cannot be implemented into applications at a real-time context. In this paper, fuzzy empirical copula is proposed to reduce the computation time of dependence structure estimation. First, a br...

This paper develops a joint copula reliability model for systems subjected to dependent competing risks caused by two degradation processes and random shocks. The two degradation processes follow gamma processes and the random shocks follow a non-homogeneous Poisson process (NHPP). Their interdependence relationship is modeled by a copula function, which is determined by a two-stage method base...