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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 give a review of the standard approaches to extreme value theory. Special focus on the tail of the distribution is underlined, in particular concerning the fat‐tails phenomenon typical of financial returns. The core of the work is then represented by a survey of models which try to overtake some problems in determining the right shaping of extreme financial returns distribution.

The paper attempts to give a broad view of the theory about the Tail of distribution of financial market returns, with a special focus on bond returns. The aim of the core work is to find and explore via data, the best solution in order to give a right estimate of the higher moments of the distribution and of the Tail index associated with particular tail shape.

The EVT approach to VaR has certain advantages over traditional parametric and non‐parametric approaches to VaR. Parametric approaches estimate VaR by fitting some distribution to a set of observed returns while non‐parametric estimate VaR by reading off the VaR from an appropriate histogram of returns. Results show how EVT allows to overtake the problems of underestimation of risk typical of standard VaR measures. In particular the paper compares with historical simulation. The difference is quite evident showing a consistent improvement of the risk measurement performance.

It is necessary to underline how the result in the paper relies on very specific assumptions and dataset feature. Back to drawbacks of EVT, it is very important then to remind how the dataset is usually and necessarily limited to sporadic extreme events. Moreover, there is no mathematical safety of claiming robust result in the absence of normality.

The purpose of this paper is to propose a grey target decision model based on cobweb area in order to overcome the effect and influence from the extreme value of the index on the decision result. However, it does not take into account the impact of the correlation between indicators on the angle of the index, and produce a certain degree decision information distortion as a result of the equal angle between the indicators. In order to solve the above problems, a novel grey decision-making model based on cone volume is proposed.

In this paper, the model uses the whitening weight function to whiten the interval grey number, and the Delphi method and the maximal entropy method are exploited to integrate the weight of the index. On the basis of this, the center of the bull’s eye, the weight and the index value are constructed as the center circle, the radius, and the high cone, respectively. The scheme is selected by the volume of the cone, the decision is made according to the order relation, and the example is utilized to prove and analyze the validity of the proposed model.

The results show that the proposed model can well improve the traditional grey target decision-making model from the modeling object and modeling method.

The method exposed in the paper can be used to deal with the grey target decision-making problems which characteristics are multi-indexes, and the attribute values are interval grey numbers.

The paper succeeds in overcoming the disadvantages of grey target decision making based on the target center distance and the cobweb area.

The purposes of this research are to study the theory and method of multi-attribute index system design and establish a set of systematic, standardized, scientific index systems for the design optimization and inspection process. The research may form the basis for a rational, comprehensive evaluation and provide the most effective way of improving the quality of management decision-making. It is of practical significance to improve the rationality and reliability of the index system and provide standardized, scientific reference standards and theoretical guidance for the design and construction of the index system.

Using modern methods such as complex networks and machine learning, a system for the quality diagnosis of index data and the classification and stratification of index systems is designed. This guarantees the quality of the index data, realizes the scientific classification and stratification of the index system, reduces the subjectivity and randomness of the design of the index system, enhances its objectivity and rationality and lays a solid foundation for the optimal design of the index system.

Based on the ideas of statistics, system theory, machine learning and data mining, the focus in the present research is on “data quality diagnosis” and “index classification and stratification” and clarifying the classification standards and data quality characteristics of index data; a data-quality diagnosis system of “data review – data cleaning – data conversion – data inspection” is established. Using a decision tree, explanatory structural model, cluster analysis, K-means clustering and other methods, classification and hierarchical method system of indicators is designed to reduce the redundancy of indicator data and improve the quality of the data used. Finally, the scientific and standardized classification and hierarchical design of the index system can be realized.

The innovative contributions and research value of the paper are reflected in three aspects. First, a method system for index data quality diagnosis is designed, and multi-source data fusion technology is adopted to ensure the quality of multi-source, heterogeneous and mixed-frequency data of the index system. The second is to design a systematic quality-inspection process for missing data based on the systematic thinking of the whole and the individual. Aiming at the accuracy, reliability, and feasibility of the patched data, a quality-inspection method of patched data based on inversion thought and a unified representation method of data fusion based on a tensor model are proposed. The third is to use the modern method of unsupervised learning to classify and stratify the index system, which reduces the subjectivity and randomness of the design of the index system and enhances its objectivity and rationality.

Previous research suggests that monthly commodity futures returns are like equity returns and recommend long-only portfolio positions. A follow-up question is whether the distributions of daily returns on commodity futures are fat-tailed, just like equity returns. This question has important implication for commodity futures traders because futures trade positions are marked to the market daily. The Extreme Value Theory (EVT) is used to test whether the distributions of the commodity futures returns are fat-tailed with finite variance. The results suggest that not all commodity futures returns have a fat-tail distribution and the tails of the distributions of commodity futures returns generally are smaller than the tails of the distribution of equity returns.

Illustrates the impact of major events on UK share prices/returns in the last 35 years and the time series trends of Asian stock markets. Looks at the impact of the 1997 Asian crisis on Asian financial markets from the US investor’s point of view, comparing 1994‐1999 data for the “tiger markets” with the mature markets of the USA, UK and Japan using a conservative investment strategy to “minimize the probability of loss”. Shows that a mixed portfolio gave higher returns than US domestic returns with less risk. Confirms this using the tail index based on extreme value theory; and shows that correlation has a positive relationship with volatility but a negative relationship with returns. Adds that, during stock market downturn, the increase in correlation and volatility may cancel out the benefits of diversification.

It seems that the Internet boom, which started at the end of the 1990s and finished with the spectacular collapse of the so-called dotcoms, is probably over. We are currently enjoying a period of fast and stable growth. This is manifested by the growing number of both Internet users and companies which – to an ever-increasing extent – use the Internet as a form of communication (both internal and external), promotion, sales etc. Expenditures on Internet advertising are growing continuously and now constitute more than 25% of all advertising expenditure. A natural consequence of this development is the need for the standardisation and organisation of the world of the Internet. These activities will result in a greater awareness of the benefits which this medium provides, increasing the possibilities of its use, and – most importantly – the opportunity to evaluate the return on investments made on the Internet. Nowadays, it is clear that many companies are striving to increase the quality of their activities on the Internet or to improve the effectiveness of such activities. As a consequence, the number of companies that look for indices which would enable the making of more precise and effective decisions in the scope of online operations is growing.

This chapter is dedicated to the phenomenon of the increasing role of the Internet in business, including the scale of its use by Polish and international companies. We present the most commonly used measures of marketing activities on the Internet and in social media. This group includes the indices which make it possible to determine whether a company actually needs a website. Other measures allow for the improvement in the effectiveness of the activity on the Internet, whereas others specify the costs of activities on the Internet and often serve as the basis for settlements between a company and advertising agencies or companies specialising in website design. It is worth emphasising that the Paid, Earned, Shared, Owned (PESO) model, worked out by Don Bartholomew,¹ is the basis for creation and description of indices concerning social media. This model has gained certain popularity in the social media industry. It does not, however, specify how individual indices should be named and calculated. It maps already existing indices and adapts them to specific levels of marketing communication measurement. All the measures indicated by the author of the model have been grouped into five major areas: exposure, engagement, brand awareness, action and recommendations. This model– similarly to all models of performance measurement – inspired by the sales funnel concept, adjusts certain standard indices and proposals of measurements for specific levels. Additionally, the measures are divided into four types, depending on who the owner of the content is: Paid (P) – refers to all forms of paid content; Owned (O) – all websites and web properties controlled by a company or brand; Earned (E) – the contents about a given brand created spontaneously by Internet users; and Shared (S) – the contents shared by Internet users.

The specific criteria to the microstructure of emerging markets such as low liquidity, very pronounced asymmetric information, and high volatility affect the risk market. Previous researchers have concluded that the calculation methods of the Value‐at‐Risk (VaR) adopted in developed markets are poorly adapted to the specific structure of emerging markets. The purpose of this paper is to see what these specific criteria of emerging markets are and whether these criteria have any impact on market risk and hedging capital. A second purpose it to see if practitioners should adjust the tools of risk measurement to the specifications of emerging markets and how the Value‐at‐Risk (VaR) should be adjusted.

The paper asks what are the specific criteria to the microstructure of emerging markets? Should we adjust the tools of risk measurement to these specifications? How do we adjust the Value‐at‐Risk (VaR)?

The paper demonstrated a market improvement in the performance of adjusted VaR. Indeed, models for measuring the VaR adjusted to liquidity and to asymmetry of information are accepted by the tests of backtesting. The term of average error has decreased.

This improvement of adjusted VaR in the performance of measuring risk implies a better estimation of the capital allocated to cover market risk.

The results from this empirical study offer an alternative approach adapted to the specific structure of emerging markets and a better estimation of the capital allocated to cover market risk.

The purpose of this paper is to propose a semiparametric estimator for the tail index of Pareto-type random truncated data that improves the existing ones in terms of mean square error. Moreover, we establish its consistency and asymptotic normality.

To construct a root mean squared error (RMSE)-reduced estimator of the tail index, the authors used the semiparametric estimator of the underlying distribution function given by Wang (1989). This allows us to define the corresponding tail process and provide a weak approximation to this one. By means of a functional representation of the given estimator of the tail index and by using this weak approximation, the authors establish the asymptotic normality of the aforementioned RMSE-reduced estimator.

In basis on a semiparametric estimator of the underlying distribution function, the authors proposed a new estimation method to the tail index of Pareto-type distributions for randomly right-truncated data. Compared with the existing ones, this estimator behaves well both in terms of bias and RMSE. A useful weak approximation of the corresponding tail empirical process allowed us to establish both the consistency and asymptotic normality of the proposed estimator.

A new tail semiparametric (empirical) process for truncated data is introduced, a new estimator for the tail index of Pareto-type truncated data is introduced and asymptotic normality of the proposed estimator is established.