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

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.

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 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.

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.

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.

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.

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.