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The purpose of this paper is to investigate the stochastic comparisons of the parallel system with independent heterogeneous Gumbel components and series and parallel systems with independent heterogeneous truncated Gumbel components in terms of various stochastic orderings.

The obtained results in this paper are obtained by using the vector majorization methods and results. First, the components of series and parallel systems are heterogeneous and having Gumbel or truncated Gumbel distributions. Second, multiple-outlier truncated Gumbel models are discussed for these systems. Then, the relationship between the systems having Gumbel components and Weibull components are considered. Finally, Monte Carlo simulations are performed to illustrate some obtained results.

The reversed hazard rate and likelihood ratio orderings are obtained for the parallel system of Gumbel components. Using these results, similar new results are derived for the series system of Weibull components. Stochastic comparisons for the series and parallel systems having truncated Gumbel components are established in terms of hazard rate, likelihood ratio and reversed hazard rate orderings. Some new results are also derived for the series and parallel systems of upper-truncated Weibull components.

To the best of our knowledge thus far, stochastic comparisons of series and parallel systems with Gumbel or truncated Gumble components have not been considered in the literature. Moreover, new results for Weibull and upper-truncated Weibull components are presented based on Gumbel case results.

From a regulatory point of view, as explained by Dimson and Marsh [1994, 1995], the amount of capital required by a financial institution to ensure an acceptably small probability of failure should depend on the risk associated with the assets detained in its portfolio. Dimson and Marsh [1994] conduct an empirical study on long and short equity trading books of securities firms acting as market makers. They consider different existing regulations: the comprehensive approach, as applied in the United States by the Securities and Exchange Commission; the building‐block approach, as proposed by the Basle Committee on Banking Supervision, and incorporated in the European Community [1992] Capital Adequacy Directive (CAD); and the portfolio approach, which in the U.K. forms part of the rules of the Securities and Futures Authority [1992]. All three methods are compared via the position risk requirement (PRR) that determines the amount of capital that financial institutions have to put aside. As shown by the authors in their empirical study, the methods proposed by the international regulators are barely related to the risk of the portfolios! Only for the national U.K. rules, the PRR and the risk of a portfolio show positive correlation.

The potential advantage of extreme value theory in modeling management phenomena is the central theme of this paper. The statistics of extremes have played only a very limited role in management studies despite the disproportionate emphasis on unusual events in the world of managers. An overview of this theory and related statistical models is presented, and illustrative empirical examples provided.

Fat‐tailed distributions have been found in many financial and economic variables ranging from forecasting returns on financial assets to modeling recovery distributions in bankruptcies. They have also been found in numerous insurance applications such as catastrophic insurance claims and in value‐at‐risk measures employed by risk managers. Financial applications include:

The purpose of this paper is to provide an analysis of the dependence structure between returns from real estate investment trusts (REITS) and a stock market index. Further, the aim is to illustrate how copula approaches can be applied to model the complex dependence structure between the assets and for risk measurement of a portfolio containing investments in REIT and equity indices.

The usually suggested multivariate normal or variance‐ covariance approach is applied, as well as various copula models in order to investigate the dependence structure between returns of Australian REITS and the Australian stock market. Different models including the Gaussian, Student t, Clayton and Gumbel copula are estimated and goodness‐of‐fit tests are conducted. For the return series, both the Gaussian and a non‐parametric estimate of the distribution is applied. A risk analysis is provided based on Monte Carlo simulations for the different models. The value‐at‐risk measure is also applied for quantification of the risks for a portfolio combining investments in real estate and stock markets.

The findings suggest that the multivariate normal model is not appropriate to measure the complex dependence structure between the returns of the two asset classes. Instead, a model using non‐parametric estimates for the return series in combination with a Student t copula is clearly more suitable. It further illustrates that the usually applied variance‐covariance approach leads to a significant underestimation of the actual risk for a portfolio consisting of investments in REITS and equity indices. The nature of risk is better captured by the suggested copula models.

To the authors', knowledge, this is one of the first studies to apply and test different copula models in real estate markets. Results help international investors and portfolio managers to deepen their understanding of the dependence structure between returns from real estate and equity markets. Additionally, the results should be helpful for implementation of a more adequate risk management for portfolios containing investments in both REITS and equity indices.

This article investigates the effect of modeling extreme events on the calculation of minimum capital risk requirements for three LIFFE futures contracts. The use of internal models will be permitted under the European Community Capital Adequacy Directive II and will be widely adopted in the near future for determining capital adequacies. Close scrutiny of competing models is required to avoid a potentially costly misallocation of capital resources, to ensure the safety of the financial system. The authors propose a semi‐parametric approach, for which extreme risks are modeled using a generalized Pareto distribution, and smaller risks are characterized by the empirically observed distribution function. The primary finding of comparing the capital requirements based on this approach with those calculated from both the unconditional density and from a conditional density (a GARCH(1,1) model), is that for both in‐sample and out‐of‐sample tests, the extreme value approach yields superior results. This is attributable to the fact that the other two models do not explicitly model the tails of the return distribution.

Extreme value model is one of the most important models that are applicable in air pollution data. This paper aims at introducing a new model of extreme value that is more suitable in environmental studies.

The parameters of the new model have been estimated by method of maximum likelihood. In order to relate to air pollution impacts, the new extreme value model was used, applied to carbon monoxide (CO) in parts per million (ppm) at several places in Malaysia. The objective of this analysis is to fit the extreme values with a new model and to examine its performance. Comparison of the new model with others is shown to illustrate the applicability of this new model.

The results show that the new model is the best fit using the method of maximum likelihood. The new model gives a significant impact of CO data, which gives the smallest standard error and p‐values. The new extreme value model is able to identify significantly problems of air pollution. The results presented by the new extreme value model can be used as an air quality management tool by providing the decision makers means to determine the required reduction of source.

The new extreme value model has mostly been applied in environmental studies for the statistical treatment of air pollution. The results of the numerical and simulated CO data indicate that the new model both is easy to use and can achieve even higher accuracy compared with other models.

The design and pricing of weather‐based insurance instruments is strongly based on an implicit assumption that the dependence structure between crop yields and weather variables remains unchanged over time. The purpose of this paper is to verify this critical assumption by employing historical time series of weather and farm yields from a semi‐arid region.

The analysis employs two different approaches to measure dependence in multivariate distributions – the regression analysis and copula approach. The estimations are done by employing Bayesian hierarchical model.

The paper reveals statistically significant temporal changes in the joint distribution of weather variables and wheat yields for grain‐producing farms in Kazakhstan over the period from 1961 to 2003.

By questioning its basic assumption the paper draws attention to serious limitations in the current methodology of the weather‐based insurance design.

The empirical results obtained indicate that the relationship between weather and crop yields is not fixed and can change over time. Accordingly, greater effort is required to capture potential temporal changes in the weather‐yield‐relationship and to consider them while developing and rating weather‐based insurance instruments.

The estimation of selected copula and regression models has been done by employing Bayesian hierarchical models.

Application of financial risk models in the emerging markets poses special challenges. A fundamental challenge is to accurately model the return distributions which are particularly fat tailed and skewed. Value-at-Risk (VaR) measures based on the Extreme Value Theory (EVT) have been suggested, but typically data histories are limited, making it hard to test and apply EVT. The chapter addresses issues in (i) modeling the VaR measure in the presence of structural breaks in an economy, (ii) the choice of stable innovation distribution with volatility clustering effects, (iii) modeling the tails of the empirical distribution, and (iv) fixing the cut-off point for isolating extreme observations. Pakistan offers an instructive case since its equity market exhibits high volatility and incidence of extreme returns. The recent Global Financial Crisis has been another source of extreme returns. The confluence of the two sources of volatility provides us with a rich data set to test the VaR/EVT model rigorously and examine practical challenges in its application in an emerging market.