CVaR sensitivity with respect to tail thickness

We consider the sensitivity of conditional value-at-risk (CVaR) with respect to the tail index assuming regularly varying tails and exponential and faster-than-exponential tail decay for the return distribution. We compare it to the CVaR sensitivity with respect to the scale parameter for stable Paretian, the Student's t, and generalized Gaussian laws and discuss implications for the modeling of daily returns and marginal rebalancing decisions. Finally, we explore empirically the impact on the asymptotic variability of the CVaR estimator with daily returns which is a standard choice for the return frequency for risk estimation. --fat-tailed distributions,regularly varying tails,conditional value-at-risk,marginal rebalancing,asymptotic variability

On a class of distributions stable under random summation

We investigate a family of distributions having a property of stability-under-addition, provided that the number $\nu$ of added-up random variables in the random sum is also a random variable. We call the corresponding property a \,$\nu$-stability and investigate the situation with the semigroup generated by the generating function of $\nu$ is commutative. Using results from the theory of iterations of analytic functions, we show that the characteristic function of such a $\nu$-stable distribution can be represented in terms of Chebyshev polynomials, and for the case of $\nu$-normal distribution, the resulting characteristic function corresponds to the hyperbolic secant distribution. We discuss some specific properties of the class and present particular examples.Comment: 12 pages, 1 figur

A Taxonomy of Essential Services

Communities, countries and alliances cannot be efficient in preparing to meet diverse threats to their security within traditional organizational stovepipes. The boundaries between ‘internal’ and ‘external’ threats are getting fuzzier, and the vulnerabilities of governments, businesses and communities feed on each other, while the comprehensive approach is gaining traction in ever more security fields. The implementation of the comprehensive approach poses a number of methodological challenges. While it clearly requires coordination of various capabilities of a multitude of actors, it is less apparent which is the suitable organising concept. This paper takes as a starting point the concept of ‘essential services’ and suggests a taxonomy, that would allow to treat threats, vulnerabilities and risk in a common comprehensive framework. The taxonomy has been developed with a specific purpose in mind, and thus refers to European Essential Services (EES). We nevertheless reason that it can be replicated to support decision making at other levels, e.g. in national security policy making and planning

Fat-tailed models for risk estimation

In the post-crisis era, financial institutions seem to be more aware of the risks posed by extreme events. Even though there are attempts to adapt methodologies drawing from the vast academic literature on the topic, there is also skepticism that fat-tailed models are needed. In this paper, we address the common criticism and discuss three popular methods for extreme risk modeling based on full distribution modeling and and extreme value theory. --

The Financial Market of Indices of Socioeconomic Wellbeing

The financial industry should be involved in mitigating the risk of downturns in the financial wellbeing indices around the world by implementing well-developed financial tools such as insurance instruments on the underlying wellbeing indices. We define a new quantitative measure of the wellbeing of a country's population for those countries using the world development indicators provided by the World Bank. We monetize the indices of socioeconomic wellbeing, which serve as "risky assets," and consequently develop a global financial market for them, which serves as a "market of indices of socioeconomic wellbeing." Then, we compare the wellbeing of different countries using financial econometric analysis and dynamic asset pricing theory. We provide the optimal portfolio weight composition along with the efficient frontiers of the wellbeing socioeconomic indices with different risk-return measures. We derive insurance instruments, such as put options, which allow the financial industry to monitor, manage, and trade these indices, creating the funds for insurance against adverse movements of those indices. Our findings should help financial institutions to incorporate socioeconomic issues as an additional dimension to their "two-dimensional" risk-return adjusted optimal financial portfolios.Comment: 33 pages, 20 figure

Audio reader of electronic music as a means of teaching high school seniors the subject «World art culture»

The article considers the problems of formation of musical culture of high school seniors and shows the educational potential of an audio reader as a learning toolВ статье рассмотрены проблемы формирования музыкальной культуры старшеклассников, показан образовательный потенциал аудио-хрестоматии как средства обучени